Osaka Journal of Mathematics Articles (Project Euclid)
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The latest articles from Osaka Journal of Mathematics on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTTue, 22 Mar 2011 10:05 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Quotients of bounded homogeneous domains by cyclic groups
http://projecteuclid.org/euclid.ojm/1277298908
<strong>Christian Miebach</strong><p><strong>Source: </strong>Osaka J. Math., Volume 47, Number 2, 331--352.</p><p><strong>Abstract:</strong><br/>
Let $D$ be a bounded homogeneous domain in $\mathbb{C}^{n}$
and let $\varphi$ be an automorphism of $D$ which generates
a discrete subgroup $\Gamma$ of $\Aut_{\mathcal{O}}(D)$. It
is shown that the complex space $D/\Gamma$ is Stein.
</p>projecteuclid.org/euclid.ojm/1277298908_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTBranched twist spins and knot determinantshttps://projecteuclid.org/euclid.ojm/1508486572<strong>Mizuki Fukuda</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 679--688.</p><p><strong>Abstract:</strong><br/>
A branched twist spin is a generalization of twist spun knots, which appeared in the study of locally smooth circle actions on the $4$-sphere due to Montgomery, Yang, Fintushel and Pao. In this paper, we give a sufficient condition to distinguish non-equivalent, non-trivial branched twist spins by using knot determinants. To prove the assertion, we give a presentation of the fundamental group of the complement of a branched twist spin, which generalizes a presentation of Plotnick, calculate the first elementary ideals and obtain the condition of the knot determinants by substituting $-1$ for the indeterminate.
</p>projecteuclid.org/euclid.ojm/1508486572_20171020040335Fri, 20 Oct 2017 04:03 EDTOn a theorem of Muraihttps://projecteuclid.org/euclid.ojm/1508486573<strong>Gabriel Navarro</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 689--690.</p><p><strong>Abstract:</strong><br/>
If $B$ is a $p$-block of a finite group $G$, then the intersection of the kernels of the height zero characters in $B$ has a normal $p$-complement.
</p>projecteuclid.org/euclid.ojm/1508486573_20171020040335Fri, 20 Oct 2017 04:03 EDTLongtime convergence for epitaxial growth model under Dirichlet conditionshttps://projecteuclid.org/euclid.ojm/1508486574<strong>Somayyeh Azizi</strong>, <strong>Gianluca Mola</strong>, <strong>Atsushi Yagi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 691--708.</p><p><strong>Abstract:</strong><br/>
This paper continues our study on the initial-boundary value problem for a semilinear parabolic equation of fourth order which has been presented by Johnson-Orme-Hunt-Graff-Sudijono-Sauder-Orr [12] to describe the large-scale features of a growing crystal surface under molecular beam epitaxy. In the preceding paper [1], we already constructed a dynamical system generated by the problem and verified that the dynamical system has a finite-dimensional attractor (especially, every trajectory has nonempty $\omega$-limit set) and admits a Lyapunov function (of the form (3.1)). This paper is then devoted to showing longtime convergence of trajectory. We shall prove that every trajectory converges to some stationary solution as $t \to \infty$. As a matter of fact, we have obtained in [10] the similar result for the equation but under the Neumann like boundary conditions $\frac{\partial u}{\partial n}=\frac\partial{\partial n}\varDelta u=0$ on the unknown function $u$. In this paper, we want as in [1] to handle the Dirichlet boundary conditions $u=\frac{\partial u}{\partial n}=0$, maybe physically more natural conditions than before.
</p>projecteuclid.org/euclid.ojm/1508486574_20171020040335Fri, 20 Oct 2017 04:03 EDTParabolic, ridge and sub-parabolic curves on implicit surfaces with singularitieshttps://projecteuclid.org/euclid.ojm/1508486575<strong>Masaru Hasegawa</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 709--723.</p><p><strong>Abstract:</strong><br/>
We study parabolic, ridge and sub-parabolic curves on implicit surfaces defined by smooth functions $\mathcal{R}$-equivalent to $A_1^-$-singularity. To investigate ridge and sub-parabolic curves, we present the local parameterizations of the implicit surfaces, and we show the asymptotic behavior of the principal curvatures and directions by using the parameterization. We also present height and distance squared functions on implicit surfaces in the appendix.
</p>projecteuclid.org/euclid.ojm/1508486575_20171020040335Fri, 20 Oct 2017 04:03 EDTOn the Morse-Novikov number for 2-Knotshttps://projecteuclid.org/euclid.ojm/1508486576<strong>Hisaaki Endo</strong>, <strong>Andrei Pajitnov</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 725--736.</p><p><strong>Abstract:</strong><br/>
Let $K\subset S^4$ be a 2-knot. The Morse-Novikov number ${\mathcal M}{\mathcal N}(K)$ is the minimal possible number of critical points of a Morse map $S^4\setminus K\to S^1$ belonging to the canonical class in $H^1(S^4\setminus K)$. We prove that for a classical knot $K\subset S^3$ the Morse-Novikov number of the spun knot $S(K)$ is $\leq 2{\mathcal M}{\mathcal N}(K)$. This enables us to compute ${\mathcal M}{\mathcal N}(S(K))$ for every classical knot $K$ with tunnel number 1.
</p>projecteuclid.org/euclid.ojm/1508486576_20171020040335Fri, 20 Oct 2017 04:03 EDTExtrinsic circular trajectories on geodesic spheres in a complex projective spacehttps://projecteuclid.org/euclid.ojm/1508486577<strong>Tuya Bao</strong>, <strong>Toshiaki Adachi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 737--747.</p><p><strong>Abstract:</strong><br/>
We say a trajectory for a Sasakian magnetic field on a geodesic sphere in a complex projective space to be extrinsic circular if it can be seen as a circle in the ambient space. We study how the moduli space of extrinsic circular trajectories behaves in the moduli space of all circles in the ambient complex projective space. As an application we characterize the geodesic sphere of special radius which lies on the boundary position of the family of Berger spheres among all geodesic spheres and that has a characteristic properties from the viewpoint of lengths of circles.
</p>projecteuclid.org/euclid.ojm/1508486577_20171020040335Fri, 20 Oct 2017 04:03 EDTProperties of the Dirac spectrum on three dimensional lens spaceshttps://projecteuclid.org/euclid.ojm/1508486578<strong>Sebastian Boldt</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 749--767.</p><p><strong>Abstract:</strong><br/>
We present a spectral rigidity result for the Dirac operator on lens spaces. More specifically, we show that each homogeneous lens space and each three dimensional lens space $L(q;p)$ with $q$ prime is completely characterized by its Dirac spectrum in the class of all lens spaces.
</p>projecteuclid.org/euclid.ojm/1508486578_20171020040335Fri, 20 Oct 2017 04:03 EDTOn ramified torsion points on a curve with stable reduction over an absolutely unramified basehttps://projecteuclid.org/euclid.ojm/1508486579<strong>Yuichiro Hoshi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 769--789.</p><p><strong>Abstract:</strong><br/>
Let $p$ be an odd prime number, $W$ an {\it absolutely unramified} $p$-adically complete discrete valuation ring with algebraically closed residue field, and $X$ a curve of genus at least two over the field of fractions $K$ of $W$. In the present paper, we study, under the assumption that $X$ has {\it stable reduction} over $W$, {\it torsion points} on $X$, i.e., torsion points of the Jacobian variety $J$ of $X$ which lie on the image of the Albanese embedding $X\hookrightarrow J$ with respect to a $K$-rational point of $X$. A consequence of the main result of the present paper is that if, moreover, $J$ has good reduction over $W$, then every torsion point on $X$ is {\it $K$-rational} {\it after multiplying $p$}. This result is closely related to a conjecture of {\it R. Coleman} concerning the ramification of torsion points. For instance, this result leads us to a solution of the conjecture in the case where a given curve is hyperelliptic and of genus at least $p$.
</p>projecteuclid.org/euclid.ojm/1508486579_20171020040335Fri, 20 Oct 2017 04:03 EDTPerturbation of irregular Weyl-Heisenberg wave packet frames in $L^2(\mathbb{R})$https://projecteuclid.org/euclid.ojm/1508486580<strong>Raj Kumar</strong>, <strong>Ashok K. SAH</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 791--801.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider the perturbation problem of irregular Weyl-Heisenberg wave packet frame $\{D_{a_j}T_{bk}E_{c_m}\psi\}_{j,k,m\in \mathbb{Z}}$ about dilation, translation and modulation parameters. We give a method to determine whether the perturbation systems is a frame for wave packet functions whose Fourier transforms have small support and prove the stability about dilation parameter on Paley-Wiener space. For a wave packet function, we give a definite answer to the stability about translation parameter $b$.
</p>projecteuclid.org/euclid.ojm/1508486580_20171020040335Fri, 20 Oct 2017 04:03 EDTRealizing homology classes up to cobordismhttps://projecteuclid.org/euclid.ojm/1508486581<strong>Mark Grant</strong>, <strong>András SZŰCS</strong>, <strong>Tamás Terpai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 803--807.</p><p><strong>Abstract:</strong><br/>
It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod $2$ homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.
</p>projecteuclid.org/euclid.ojm/1508486581_20171020040335Fri, 20 Oct 2017 04:03 EDTGroups of automorphisms of bordered orientable Klein surfaces of topological genus 2https://projecteuclid.org/euclid.ojm/1508486582<strong>E. Bujalance</strong>, <strong>J.J. Etayo</strong>, <strong>E. Martínez</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 809--824.</p><p><strong>Abstract:</strong><br/>
In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.
</p>projecteuclid.org/euclid.ojm/1508486582_20171020040335Fri, 20 Oct 2017 04:03 EDTThe arc metric on Teichmüller spaces of surfaces of infinite type with boundaryhttps://projecteuclid.org/euclid.ojm/1515661214<strong>Qiyu Chen</strong>, <strong>Lixin Liu</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 1--38.</p><p><strong>Abstract:</strong><br/>
Let $X_{0}$ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric (which is called arc metric) on the quasiconformal Teichmüller space $\mathcal{T}(X_{0})$ provided that $X_{0}$ satisfies a geometric condition. Furthermore, we construct several examples of hyperbolic surfaces of infinite type satisfying the geometric condition and discuss the relation between the Shiga's condition and the geometric condition.
</p>projecteuclid.org/euclid.ojm/1515661214_20180111040034Thu, 11 Jan 2018 04:00 ESTOn five dimensional Sasakian Lie algebras with trivial centerhttps://projecteuclid.org/euclid.ojm/1515661215<strong>E. Loiudice</strong>, <strong>A. Lotta</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 39--49.</p><p><strong>Abstract:</strong><br/>
We show that every five-dimensional Sasakian Lie algebra with trivial center is $\varphi$-symmetric. Moreover starting from a particular Sasakian structure on the Lie group $SL(2,\mathbb{R})\times\text{Aff}(\mathbb{R})$ we obtain a family of contact metric $(k,\mu)$ structures whose Boeckx invariants assume all values less than $-1$.
</p>projecteuclid.org/euclid.ojm/1515661215_20180111040034Thu, 11 Jan 2018 04:00 ESTGlobal existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear productionhttps://projecteuclid.org/euclid.ojm/1515661216<strong>Etsushi Nakaguchi</strong>, <strong>Koichi Osaki</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 51--70.</p><p><strong>Abstract:</strong><br/>
We study the global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth. We introduce superlinear production of a chemoattractant. We then show the global existence of solutions in $L_p$ space $( p > n )$ under certain relations between the degradation and production orders.
</p>projecteuclid.org/euclid.ojm/1515661216_20180111040034Thu, 11 Jan 2018 04:00 ESTRepresentations of quantized coordinate algebras via PBW-type elementshttps://projecteuclid.org/euclid.ojm/1515661217<strong>Hironori Oya</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 71--115.</p><p><strong>Abstract:</strong><br/>
Inspired by the work of Kuniba-Okado-Yamada, we study some tensor product representations of quantized coordinate algebras of symmetrizable Kac-Moody Lie algebras in terms of quantized enveloping algebras. As a consequence, we describe structures and properties of certain reducible representations of quantized coordinate algebras. This paper includes alternative proofs of Soibelman's tensor product theorem and Kuniba-Okado-Yamada's common structure theorem based on our direct calculation method using global bases.
</p>projecteuclid.org/euclid.ojm/1515661217_20180111040034Thu, 11 Jan 2018 04:00 ESTAsymptotic behavior of the solutions for the Laplace equation with a large spectral parameter and the inhomogeneous Robin type conditionshttps://projecteuclid.org/euclid.ojm/1515661218<strong>Masaru Ikehata*</strong>, <strong>Mishio Kawashita**</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 117--163.</p><p><strong>Abstract:</strong><br/>
Reduced problems are elliptic problems with a large parameter (as the spectral parameter) given by the Laplace transform of time dependent problems. In this paper, asymptotic behavior of the solutions of the reduced problem for the classical heat equation in bounded domains with the inhomogeneous Robin type conditions is discussed. The boundary of the domain consists of two disjoint surfaces, outside one and inside one. When there are inhomogeneous Robin type data at both boundaries, it is shown that asymptotics of the value of the solution with respect to the large parameter at a given point inside the domain is closely connected to the distance from the point to the both boundaries. It is also shown that if the inside boundary is strictly convex and the data therein vanish, then the asymptotics is different from the previous one. The method for the proof employs a representation of the solution via single layer potentials. It is based on some non trivial estimates on the integral kernels of related integral equations which are previously established and used in studying an inverse problem for the heat equation via the enclosure method.
</p>projecteuclid.org/euclid.ojm/1515661218_20180111040034Thu, 11 Jan 2018 04:00 ESTA rigidity of equivariant holomorphic maps into a complex Grassmannian induced from orthogonal direct sums of holomorphic line bundleshttps://projecteuclid.org/euclid.ojm/1515661219<strong>Isami Koga</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 165--176.</p><p><strong>Abstract:</strong><br/>
In the present paper, we study holomorphic maps induced from orthogonal direct sums of holomorphic line bundles over a compact simply connected homogeneous Kähler manifold into a complex Grassmannian. Then we show if such maps are equivariant, then they are unique up to complex isometry.
</p>projecteuclid.org/euclid.ojm/1515661219_20180111040034Thu, 11 Jan 2018 04:00 EST$\delta$-homogeneity in Finsler geometry and the positive curvature problemhttps://projecteuclid.org/euclid.ojm/1515661220<strong>Ming Xu</strong>, <strong>Lei Zhang*</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 177--194.</p><p><strong>Abstract:</strong><br/>
In this paper, we explore the similarity between normal homogeneity and $\delta$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space is $G$-$\delta$-homogeneous, for some suitably chosen connected quasi-compact $G$. So $\delta$-homogeneous Finsler metrics can be defined by a bi-invariant singular metric on $G$ and submersion, just as normal homogeneous metrics, using a bi-invariant Finsler metric on $G$ instead. More careful analysis shows, in the space of all Finsler metrics on $G/H$, the subset of all $G$-$\delta$-homogeneous ones is in fact the closure for the subset of all $G$-normal ones, in the local $C^0$-topology (Theorem 1.1). Using this approximation technique, the classification work for positively curved normal homogeneous Finsler spaces can be applied to classify positively curved $\delta$-homogeneous Finsler spaces, which provides the same classification list. As a by-product, this argument tells more about $\delta$-homogeneous Finsler metrics satisfying the (FP) condition (a weaker version of positively curved condition).
</p>projecteuclid.org/euclid.ojm/1515661220_20180111040034Thu, 11 Jan 2018 04:00 ESTÉtale endomorphisms of 3-folds. Ihttps://projecteuclid.org/euclid.ojm/1524038727<strong>Yoshio Fujimoto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 195--257.</p><p><strong>Abstract:</strong><br/>
This paper is the first part of our project towards classifications of smooth projective $3$-folds $X$ with $\kappa(X) = -\infty$ admitting a non-isomorphic étale endomorphism. We can prove that for any extremal ray $R$ of divisorial type, the contraction morphism $\pi_R\colon X\to X'$ associated to $R$ is the blowing-up of a smooth $3$-fold $X'$ along an elliptic curve. The difficulty is that there may exist infinitely many extremal rays on $X$. Thus we introduce the notion of an `ESP' which is an infinite sequence of non-isomorphic finite étale coverings of $3$-folds with constant Picard number. We can run the minimal model program (`MMP') with respect to an ESP and obtain the `FESP' $Y_{\bullet}$ of $(X, f)$ which is a distinguished ESP with \textit{extremal rays of fiber type} (cf. Definition 3.6). We first classify $Y_{\bullet}$ and then blow-up $Y_{\bullet}$ along elliptic curves to recover the original $X$. The finiteness of extremal rays of $\overline{\rm NE}(X)$ is verified in certain cases (cf. Theorem 1.4). We encounter a new phenomenon showing that our \'{e}taleness assumption is related with torsion line bundles on an elliptic curve (cf. Theorem 1.5).
</p>projecteuclid.org/euclid.ojm/1524038727_20180418040536Wed, 18 Apr 2018 04:05 EDTGalois covers of type $(p,\cdots,p)$, vanishing cycles formula, and the existence of torsor structureshttps://projecteuclid.org/euclid.ojm/1524038728<strong>Mohamed Saïdi</strong>, <strong>Nicholas Williams</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 259--296.</p><p><strong>Abstract:</strong><br/>
In this article we prove a local Riemman-Hurwitz formula which compares the dimensions of the spaces of vanishing cycles in a finite Galois cover of type $(p,p,\cdots,p)$ between formal germs of $p$-adic curves and which generalises the formula proven in [6] in the case of Galois covers of degree $p$. We also investigate the problem of the existence of a torsor structure for a finite Galois cover of type $(p,p,\cdots,p)$ between $p$-adic schemes.
</p>projecteuclid.org/euclid.ojm/1524038728_20180418040536Wed, 18 Apr 2018 04:05 EDTOn calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-linkshttps://projecteuclid.org/euclid.ojm/1524038729<strong>Atsushi Ishii</strong>, <strong>Ryo Nikkuni</strong>, <strong>Kanako Oshiro</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 297--313.</p><p><strong>Abstract:</strong><br/>
There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remarks to calculate the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links, and observe their behaviors. For spatial graphs, we calculate the invariants of Suzuki's theta-curves and show that the invariants are nontrivial for Suzuki's theta-curves whose Alexander ideals are trivial. For handlebody-knots, we give a remark on abelianizations and calculate the invariant of the handlebody-knots up to six crossings. For surface-links, we correct Yoshikawa's table and calculate the invariants of the surface-links in the table.
</p>projecteuclid.org/euclid.ojm/1524038729_20180418040536Wed, 18 Apr 2018 04:05 EDTOn the digital representation of integers with bounded prime factorshttps://projecteuclid.org/euclid.ojm/1524038730<strong>Yann Bugeaud</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 315--324.</p><p><strong>Abstract:</strong><br/>
Let $b \ge 2$ be an integer. Not much is known on the representation in base $b$ of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which is not a multiple of $b$ and has only small (in a suitable sense) prime factors has at least four nonzero digits in its representation in base $b$.
</p>projecteuclid.org/euclid.ojm/1524038730_20180418040536Wed, 18 Apr 2018 04:05 EDTBiharmonic submanifolds in a Riemannian manifoldhttps://projecteuclid.org/euclid.ojm/1524038731<strong>Norihito Koiso</strong>, <strong>Hajime Urakawa</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 325--346.</p><p><strong>Abstract:</strong><br/>
In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal curvatures are simple, and the associated frame field is irreducible.
</p>projecteuclid.org/euclid.ojm/1524038731_20180418040536Wed, 18 Apr 2018 04:05 EDTComparison theorems in pseudo-Hermitian geometry and applicationshttps://projecteuclid.org/euclid.ojm/1524038732<strong>Yuxin Dong</strong>, <strong>Wei Zhang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 347--367.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the theory of geodesics with respect to the Tanaka-Webster connection in a pseudo-Hermitian manifold, aiming to generalize some comparison results in Riemannian geometry to the case of pseudo-Hermitian geometry. Some Hopf-Rinow type, Cartan-Hadamard type and Bonnet-Myers type results are established.
</p>projecteuclid.org/euclid.ojm/1524038732_20180418040536Wed, 18 Apr 2018 04:05 EDTType numbers of quaternion hermitian forms and supersingular abelian varietieshttps://projecteuclid.org/euclid.ojm/1524038733<strong>Tomoyoshi Ibukiyama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 369--384.</p><p><strong>Abstract:</strong><br/>
The word \textit{type number} of an algebra means classically the number of isomorphism classes of maximal orders in the algebra, but here we consider quaternion hermitian lattices in a fixed genus and their right orders. Instead of inner isomorphism classes of right orders, we consider isomorphism classes realized by similitudes of the quaternion hermitian forms.The number $T$ of such isomorphism classes are called \textit{type number} or \textit{$G$-type number}, where $G$ is the group of quaternion hermitian similitudes. We express $T$ in terms of traces of some special Hecke operators. This is a generalization of the result announced in [5] (I) from the principal genus to general lattices. We also apply our result to the number of isomorphism classes of any polarized superspecial abelian varieties which have a model over ${\Bbb F}_p$ such that the polarizations are in a "fixed genus of lattices". This is a generalization of [8] and has an application to the number of components in the supersingular locus which are defined over ${\Bbb F}_p$.
</p>projecteuclid.org/euclid.ojm/1524038733_20180418040536Wed, 18 Apr 2018 04:05 EDTA remark on conditions that a diffusion in the natural scale is a martingalehttps://projecteuclid.org/euclid.ojm/1524038734<strong>Yuuki Shimizu</strong>, <strong>Fumihiko Nakano</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 385--391.</p><p><strong>Abstract:</strong><br/>
We consider a diffusion processes $\{ X_t \}$ on an interval in the natural scale. Some results are known under which $\{ X_t \}$ is a martingale, and we give simple and analytic proofs for them.
</p>projecteuclid.org/euclid.ojm/1524038734_20180418040536Wed, 18 Apr 2018 04:05 EDTOn the flat geometry of the cuspidal edgehttps://projecteuclid.org/euclid.ojm/1530691235<strong>Raúl Oset Sinha</strong>, <strong>Farid Tari</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 393--421.</p><p><strong>Abstract:</strong><br/>
We study the geometry of the cuspidal edge $M$ in $\mathbb{R}^3$ derived from its contact with planes and lines (referred to as flat geometry). The contact of $M$ with planes is measured by the singularities of the height functions on $M$. We classify submersions on a model of $M$ by diffeomorphisms and recover the contact of $M$ with planes from that classification. The contact of $M$ with lines is measured by the singularities of orthogonal projections of $M$. We list the generic singularities of the projections and obtain the generic deformations of the apparent contour (profile) when the direction of projection varies locally in $S^2$. We also relate the singularities of the height functions and of the projections to some geometric invariants of the cuspidal edge.
</p>projecteuclid.org/euclid.ojm/1530691235_20180704040042Wed, 04 Jul 2018 04:00 EDTBloch's conjecture for Enriques varietieshttps://projecteuclid.org/euclid.ojm/1530691236<strong>Robert Laterveer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 423--438.</p><p><strong>Abstract:</strong><br/>
Enriques varieties have been defined as higher-dimensional generalizations of Enriques surfaces. Bloch's conjecture implies that Enriques varieties should have trivial Chow group of zero-cycles. We prove this is the case for all known examples of irreducible Enriques varieties of index larger than $2$. The proof is based on results concerning the Chow motive of generalized Kummer varieties.
</p>projecteuclid.org/euclid.ojm/1530691236_20180704040042Wed, 04 Jul 2018 04:00 EDTRank-one Perturbation of Weighted Shifts on a Directed Tree: Partial Normality and Weak Hyponormalityhttps://projecteuclid.org/euclid.ojm/1530691237<strong>George R. Exner</strong>, <strong>Il Bong Jung</strong>, <strong>Eun Young Lee</strong>, <strong>Minjung Seo</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 439--462.</p><p><strong>Abstract:</strong><br/>
A special rank-one perturbation $S_{t,n}$ of a weighted shift on a directed tree is constructed. Partial normality and weak hyponormality (including quasinormality, $p$-hyponormality, $p$-paranormality, absolute-$p$-paranormality and $A(p)$-class) of $S_{t,n}$ are characterized.
</p>projecteuclid.org/euclid.ojm/1530691237_20180704040042Wed, 04 Jul 2018 04:00 EDTOn-diagonal Heat Kernel Lower Bound for Strongly Local Symmetric Dirichlet Formshttps://projecteuclid.org/euclid.ojm/1530691238<strong>Shuwen Lou</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 463--477.</p><p><strong>Abstract:</strong><br/>
This paper studies strongly local symmetric Dirichlet forms on general measure spaces. The underlying space is equipped with the intrinsic metric induced by the Dirichlet form, with respect to which the metric measure space does not necessarily satisfy volume-doubling property. Assuming Nash-type inequality, it is proved in this paper that outside a properly exceptional set, if a pointwise on-diagonal heat kernel upper bound in terms of the volume function is known a priori, then the comparable heat kernel lower bound also holds. The only assumption made on the volume growth rate is that it can be bounded by a continuous function satisfying doubling property, in other words, is not exponential.
</p>projecteuclid.org/euclid.ojm/1530691238_20180704040042Wed, 04 Jul 2018 04:00 EDTMazur manifolds and corks with small shadow complexitieshttps://projecteuclid.org/euclid.ojm/1530691239<strong>Hironobu Naoe</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 479--498.</p><p><strong>Abstract:</strong><br/>
In this paper we show that there exist infinitely many Mazur type manifolds and corks with shadow complexity one among the 4-manifolds constructed from contractible special polyhedra having one true vertex by using the notion of Turaev's shadow. We also find such manifolds among 4-manifolds constructed from Bing's house. Our manifolds with shadow complexity one contain the Mazur manifolds $W^{\pm }(l,k)$ which were studied by Akbulut and Kirby.
</p>projecteuclid.org/euclid.ojm/1530691239_20180704040042Wed, 04 Jul 2018 04:00 EDTOn Kohnen plus-space of Jacobi forms of half integral weight of matrix indexhttps://projecteuclid.org/euclid.ojm/1530691240<strong>Shuichi Hayashida</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 499--522.</p><p><strong>Abstract:</strong><br/>
We introduce a plus-space of Jacobi forms, which is a certain subspace of Jacobi forms of half-integral weight of matrix index. This is an analogue to the Kohnen plus-space in the framework of Jacobi forms. We shall show a linear isomorphism between the plus-space of Jacobi forms and the space of Jacobi forms of integral weight of certain matrix index. Moreover, we shall show that this linear isomorphism is compatible with the action of Hecke operators of both spaces. This result is a kind of generalization of Eichler-Zagier-Ibukiyama correspondence, which is an isomorphism between the generalized plus-space of Siegel modular forms of general degree and Jacobi forms of index $1$ of general degree.
</p>projecteuclid.org/euclid.ojm/1530691240_20180704040042Wed, 04 Jul 2018 04:00 EDTAnswer to a Question by Nakamura, Nakanishi, and Satoh involving crossing numbers of knotshttps://projecteuclid.org/euclid.ojm/1530691241<strong>Jun Ge</strong>, <strong>Xian'an Jin</strong>, <strong>Louis H. Kauffman</strong>, <strong>Pedro Lopes</strong>, <strong>Lianzhu Zhang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 523--527.</p><p><strong>Abstract:</strong><br/>
In this paper we give a positive answer to a question raised by Nakamura, Nakanishi, and Satoh concerning an inequality involving crossing numbers of knots. We show it is an equality only for the trefoil and for the figure-eight knots.
</p>projecteuclid.org/euclid.ojm/1530691241_20180704040042Wed, 04 Jul 2018 04:00 EDT$L^2$-Burau maps and $L^2$-Alexander torsionshttps://projecteuclid.org/euclid.ojm/1530691242<strong>Fathi Ben Aribi</strong>, <strong>Anthony Conway</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 529--545.</p><p><strong>Abstract:</strong><br/>
It is well known that the Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define $L^2$-Burau maps and use them to compute some $L^2$-Alexander torsions of links. As an application, we prove that the $L^2$-Burau maps distinguish more braids than the Burau representation.
</p>projecteuclid.org/euclid.ojm/1530691242_20180704040042Wed, 04 Jul 2018 04:00 EDTInitial-boundary value problem for the degenerate hyperbolic equation of a hanging stringhttps://projecteuclid.org/euclid.ojm/1530691243<strong>Masahiro Takayama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 547--565.</p><p><strong>Abstract:</strong><br/>
We consider an initial-boundary value problem for the degenerate linear hyperbolic equation as a model of the motion of an inextensible string fixed at one end in the gravity field. We shall show the existence and the uniqueness of the solution and study the regularity of the solution.
</p>projecteuclid.org/euclid.ojm/1530691243_20180704040042Wed, 04 Jul 2018 04:00 EDTA complete description of the antipodal set of most symmetric spaces of compact typehttps://projecteuclid.org/euclid.ojm/1530691244<strong>Jonas Beyrer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 567--586.</p><p><strong>Abstract:</strong><br/>
It is known that the antipodal set of a Riemannian symmetric space of compact type $G/K$ consists of a union of $K$-orbits. We determine the dimensions of these $K$-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we are not going to deal with are those with restricted root system $\mathfrak{a}_r$ and a non-trivial fundamental group, which is not isomorphic to $\mathbb{Z}_2$ or $\mathbb{Z}_{r+1}$. For example, we show that the antipodal sets of the Lie groups $Spin(2r+1)\:\: r\geq 5$, $E_8$ and $G_2$ consist only of one orbit which is of dimension $2r$, 128 and 6, respectively; $SO(2r+1)$ has also an antipodal set of dimension $2r$; and the Grassmannian $Gr_{r,r+q}(\mathbb{R})$ has a $rq$-dimensional orbit as antipodal set if $r\geq 5$ and $r\neq q>0$.
</p>projecteuclid.org/euclid.ojm/1530691244_20180704040042Wed, 04 Jul 2018 04:00 EDTOn the moment-angle manifold constructed by Fan, Chen, Ma and Wanghttps://projecteuclid.org/euclid.ojm/1539158659<strong>Kouyemon Iriye</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 587--593.</p><p><strong>Abstract:</strong><br/>
Fan, Chen, Ma and Wang [5] constructed a moment-angle manifold whose cohomology ring is isomorphic to that of the connected sum of sphere products consisting of one product of three spheres. In this paper, we show that these are in fact diffeomorphic.
</p>projecteuclid.org/euclid.ojm/1539158659_20181010040459Wed, 10 Oct 2018 04:04 EDTOn spectral measures of random Jacobi matriceshttps://projecteuclid.org/euclid.ojm/1539158661<strong>Trinh Khanh Duy</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 595--617.</p><p><strong>Abstract:</strong><br/>
The paper studies the limiting behaviour of spectral measures of random Jacobi matrices of Gaussian, Wishart and MANOVA beta ensembles. We show that the spectral measures converge weakly to a limit distribution which is the semicircle distribution, Marchenko-Pastur distributions or Kesten-McKay distributions, respectively. The Gaussian fluctuation around the limit is then investigated.
</p>projecteuclid.org/euclid.ojm/1539158661_20181010040459Wed, 10 Oct 2018 04:04 EDTA Danilov-type formula for toric origami manifolds via localization of indexhttps://projecteuclid.org/euclid.ojm/1539158664<strong>Hajime Fujita</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 619--645.</p><p><strong>Abstract:</strong><br/>
We give a direct geometric proof of a Danilov-type formula for toric origami manifolds by using the localization of Riemann-Roch number.
</p>projecteuclid.org/euclid.ojm/1539158664_20181010040459Wed, 10 Oct 2018 04:04 EDTAnalysis of Contact Cauchy--Riemann maps I: a priori $C^k$ estimates and asymptotic convergencehttps://projecteuclid.org/euclid.ojm/1539158665<strong>Yong-Geun Oh</strong>, <strong>Rui Wang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 647--679.</p><p><strong>Abstract:</strong><br/>
In the present article, we develop tensorial analysis for solutions $w$ of the following nonlinear elliptic system $$ {\overline \partial}^\pi w = 0, \, d(w^*\lambda \circ j) = 0, $$ associated to a contact triad $(M,\lambda,J)$. The novel aspect of this approach is that we work directly with this elliptic system on the contact manifold without involving the symplectization process. In particular, when restricted to the case where the one-form $w^*\lambda \circ j$ is exact, all a priori estimates for $w$-component can be written in terms of the map $w$ itself without involving the coordinate from the symplectization. We establish a priori $C^k$ coercive pointwise estimates for all $k \geq 2$ in terms of the energy density $\|dw\|^2$ by means of tensorial calculations on the contact manifold itself. Further, for any solution $w$ under the finite $\pi$-energy assumption and the derivative bound, we also establish the asymptotic subsequence convergence to `spiraling' instantons along the `rotating' Reeb orbit.
</p>projecteuclid.org/euclid.ojm/1539158665_20181010040459Wed, 10 Oct 2018 04:04 EDTInfinite algebraic subgroups of the real Cremona grouphttps://projecteuclid.org/euclid.ojm/1539158666<strong>Maria Fernanda Robayo</strong>, <strong>Susanna Zimmermann</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 681--712.</p><p><strong>Abstract:</strong><br/>
We give the classification of the maximal infinite algebraic subgroups of the real Cremona group of the plane up to conjugacy and present a parametrisation space of each conjugacy class. Moreover, we show that the real plane Cremona group is not generated by a countable union of its infinite algebraic subgroups.
</p>projecteuclid.org/euclid.ojm/1539158666_20181010040459Wed, 10 Oct 2018 04:04 EDTBergman iteration and $C^{\infty}$-convergence towards Kähler-Ricci flowhttps://projecteuclid.org/euclid.ojm/1539158667<strong>Ryosuke Takahashi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 713--729.</p><p><strong>Abstract:</strong><br/>
On a polarized manifold $(X,L)$, the Bergman iteration $\phi_k^{(m)}$ is defined as a sequence of Bergman metrics on $L$ with two integer parameters $k, m$. We study the relation between the Kähler-Ricci flow $\phi_t$ at any time $t \geq 0$ and the limiting behavior of metrics $\phi_k^{(m)}$ when $m=m(k)$ and the ratio $m/k$ approaches to $t$ as $k \to \infty$. Mainly, three settings are investigated: the case when $L$ is a general polarization on a Calabi-Yau manifold $X$ and the case when $L=\pm K_X$ is the (anti-) canonical bundle. Recently, Berman showed that the convergence $\phi_k^{(m)} \to \phi_t$ holds in the $C^0$-topology, in particular, the convergence of curvatures holds in terms of currents. In this paper, we extend Berman's result and show that this convergence actually holds in the smooth topology.
</p>projecteuclid.org/euclid.ojm/1539158667_20181010040459Wed, 10 Oct 2018 04:04 EDTCosmetic banding on knots and linkshttps://projecteuclid.org/euclid.ojm/1539158668<strong>Kazuhiro Ichihara</strong>, <strong>In Dae Jong</strong>, <strong>Hidetoshi Masai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 731--745.</p><p><strong>Abstract:</strong><br/>
We present various examples of cosmetic bandings on knots and links, that is, bandings on knots and links leaving their types unchanged. As a byproduct, we give a hyperbolic knot which admits exotic chirally cosmetic surgeries yielding hyperbolic manifolds. This gives a counterexample to a conjecture raised by Bleiler, Hodgson and Weeks.
</p>projecteuclid.org/euclid.ojm/1539158668_20181010040459Wed, 10 Oct 2018 04:04 EDTToric weak Fano varieties associated to building setshttps://projecteuclid.org/euclid.ojm/1539158669<strong>Yusuke Suyama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 747--760.</p><p><strong>Abstract:</strong><br/>
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a building set to be weak Fano in terms of the building set.
</p>projecteuclid.org/euclid.ojm/1539158669_20181010040459Wed, 10 Oct 2018 04:04 EDTSelf-intersections of curves on a surface and Bernoulli numbershttps://projecteuclid.org/euclid.ojm/1539158670<strong>Shinji Fukuhara</strong>, <strong>Nariya Kawazumi</strong>, <strong>Yusuke Kuno</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 761--768.</p><p><strong>Abstract:</strong><br/>
We study an operation which measures self-intersections of curves on an oriented surface. It turns out that a certain computation on this topological operation is related to the Bernoulli numbers $B_m$, and our study yields a family of explicit formulas for $B_m$. As a special case, this family contains the celebrated formula for $B_m$ due to Kronecker.
</p>projecteuclid.org/euclid.ojm/1539158670_20181010040459Wed, 10 Oct 2018 04:04 EDTThe vertices of the components of the permutation module induced from parabolic groupshttps://projecteuclid.org/euclid.ojm/1539158671<strong>Lars Pforte</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 769--775.</p><p><strong>Abstract:</strong><br/>
We consider the permutation module $k_P{\uparrow^{{\rm GL}_n(p^f)}}$, where $P$ is a parabolic group in the general linear group ${\rm GL}_n(p^f)$ and $k$ is an algebraically closed field of prime characteristic $p$. The vertices of the components of these modules have been calculated in [9] by Tinberg, who studied these modules for all groups with split BN-pairs in characteristic $p$. In this paper we show that the idea of suitability is strong enough to find all $p$-groups that are vertex of some component of $k_P{\uparrow^{{\rm GL}_n(p^f)}}$. Furthermore using a result of Burry and Carlson we show that all components have a different vertex.
</p>projecteuclid.org/euclid.ojm/1539158671_20181010040459Wed, 10 Oct 2018 04:04 EDTZero noise limit of a stochastic differential equation involving a local timehttps://projecteuclid.org/euclid.ojm/1539158672<strong>Kazumasa Kuwada</strong>, <strong>Taro Matsumura</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 777--794.</p><p><strong>Abstract:</strong><br/>
This paper studies the zero noise limit for the solution of a class of one-dimensional stochastic differential equations involving local time with irregular drift. These solutions are expected to approach one of the solutions to the ordinary differential equation formally obtained by cutting off the noise term. By determining the limit, we reveal that the presence of the local time really affects the asymptotic behavior, while it is observed only when intensity of the drift term is close to symmetric around the irregular point. Related with this problem, we also establish the Wentzel-Freidlin type large deviation principle.
</p>projecteuclid.org/euclid.ojm/1539158672_20181010040459Wed, 10 Oct 2018 04:04 EDTon the complexity of finite subgraphs of the curve graphhttps://projecteuclid.org/euclid.ojm/1539158673<strong>Edgar A. Bering IV</strong>, <strong>Gabriel Conant</strong>, <strong>Jonah Gaster</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 795--808.</p><p><strong>Abstract:</strong><br/>
We say a graph has property $\mathcal{P}_{g,p}$ when it is an induced subgraph of the curve graph of a surface of genus $g$ with $p$ punctures. Two well-known graph invariants, the chromatic and clique numbers, can provide obstructions to $\mathcal{P}_{g,p}$. We introduce a new invariant of a graph, the \emph{nested complexity length}, which provides a novel obstruction to $\mathcal{P}_{g,p}$. For the curve graph this invariant captures the topological complexity of the surface in graph-theoretic terms; indeed we show that its value is $6g-6+2p$, i.e. twice the size of a maximal multicurve on the surface. As a consequence we show that large `half-graphs' do not have $\mathcal{P}_{g,p}$, and we deduce quantitatively that almost all finite graphs which pass the chromatic and clique tests do not have $\mathcal{P}_{g,p}$. We also reinterpret our obstruction in terms of the first-order theory of the curve graph, and in terms of RAAG subgroups of the mapping class group (following Kim and Koberda). Finally, we show that large complete multipartite graphs cannot have $\mathcal{P}_{g,p}$. This allows us to compute the upper density of the curve graph, and to conclude that clique size, chromatic number, and nested complexity length are not sufficient to determine $\mathcal{P}_{g,p}$.
</p>projecteuclid.org/euclid.ojm/1539158673_20181010040459Wed, 10 Oct 2018 04:04 EDTNon-flat totally geodesic surfaces in symmetric spaces of classical typehttps://projecteuclid.org/euclid.ojm/1547607623<strong>Katsuya Mashimo</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 1--32.</p><p><strong>Abstract:</strong><br/>
We give a classification of non-flat totally geodesic surfaces in compact Riemannian symmetric spaces of classical type.
</p>projecteuclid.org/euclid.ojm/1547607623_20190115220101Tue, 15 Jan 2019 22:01 ESTOn Hochster's formula for a class of quotient spaces of moment-angle complexeshttps://projecteuclid.org/euclid.ojm/1547607624<strong>Li Yu</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 33--50.</p><p><strong>Abstract:</strong><br/>
Any finite simplicial complex $\mathcal{K}$ and a partition of the vertex set of $\mathcal{K}$ determines a canonical quotient space of the moment-angle complex of ${\mathcal K}$. We prove that the cohomology groups of such a space can be computed via some Hochster's type formula, which generalizes the usual Hochster's formula for the cohomology groups of moment-angle complexes. In addition, we show that the stable decomposition of moment-angle complexes can also be extended to such spaces. This type of spaces include all the quasitoric manifolds that are pullback from the linear models. And we prove that the moment-angle complex associated to a finite simplicial poset is always homotopy equivalent to one of such spaces.
</p>projecteuclid.org/euclid.ojm/1547607624_20190115220101Tue, 15 Jan 2019 22:01 ESTThe virtual Thurston seminorm of 3-manifoldshttps://projecteuclid.org/euclid.ojm/1547607625<strong>Michel Boileau</strong>, <strong>Stefan Friedl</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 51--63.</p><p><strong>Abstract:</strong><br/>
We show that the Thurston seminorms of all finite covers of an aspherical 3-manifold determine whether it is a graph manifold, a mixed 3-manifold or hyperbolic.
</p>projecteuclid.org/euclid.ojm/1547607625_20190115220101Tue, 15 Jan 2019 22:01 ESTPositivity of anticanonical divisors from the viewpoint of Fano conic bundleshttps://projecteuclid.org/euclid.ojm/1547607626<strong>E. A. Romano</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 65--74.</p><p><strong>Abstract:</strong><br/>
We give the first examples of flat fiber type contractions of Fano manifolds onto varieties that are not weak Fano, and we prove that these morphisms are Fano conic bundles. We also review some known results about the interaction between the positivity properties of anticanonical divisors of varieties of contractions.
</p>projecteuclid.org/euclid.ojm/1547607626_20190115220101Tue, 15 Jan 2019 22:01 ESTOn generalized Dold manifoldshttps://projecteuclid.org/euclid.ojm/1547607627<strong>Avijit Nath</strong>, <strong>Parameswaran Sankaran</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 75--90.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a smooth manifold with a (smooth) involution $\sigma:X\to X$ such that ${\rm Fix}(\sigma)\ne \emptyset$. We call the space $P(m,X):=\mathbb{S}^m\times X/\!\sim$ where $(v,x)\sim (-v,\sigma(x))$ a generalized Dold manifold. When $X$ is an almost complex manifold and the differential $T\sigma: TX\to TX$ is conjugate complex linear on each fibre, we obtain a formula for the Stiefel-Whitney polynomial of $P(m,X)$ when $H^1(X;\mathbb{Z}_2)=0$. We obtain results on stable parallelizability of $P(m,X)$ and a very general criterion for the (non) vanishing of the unoriented cobordism class $[P(m,X)]$ in terms of the corresponding properties for $X$. These results are applied to the case when $X$ is a complex flag manifold.
</p>projecteuclid.org/euclid.ojm/1547607627_20190115220101Tue, 15 Jan 2019 22:01 ESTAbelian subgroups of the mapping class groups for non-orientable surfaceshttps://projecteuclid.org/euclid.ojm/1547607628<strong>Erika Kuno</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 91--100.</p><p><strong>Abstract:</strong><br/>
One of the basic and important problems to study algebraic structures of the mapping class groups is finding abelian subgroups included in the mapping class groups. Birman-Lubotzky-McCarthy gave the answer of this question for the orientable surfaces, namely, they proved that any abelian subgroup of the mapping class groups for orientable surfaces of genus $g$ with $b$ boundary components and $c$ connected components is finitely generated and the maximal torsion-free rank of it is $3g+b-3c$. In the present paper, we prove that any abelian subgroup of the mapping class group of a compact connected non-orientable surface $N$ of genus $g\geq 1$ with $n\geq 0$ boundary components whose Euler characteristic is negative is finitely generated and the maximal torsion-free rank of it is $\frac{3}{2}(g-1)+n-2$ if $g$ is odd and $\frac{3}{2}g+n-3$ if $g$ is even.
</p>projecteuclid.org/euclid.ojm/1547607628_20190115220101Tue, 15 Jan 2019 22:01 ESTParametrization for a class of Rauzy Fractalshttps://projecteuclid.org/euclid.ojm/1547607629<strong>J. Bastos</strong>, <strong>T. Rodrigues de Souza</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 101--122.</p><p><strong>Abstract:</strong><br/>
In this paper, we study a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we give explicitly an automaton that generates the boundary of ${\mathcal R}_a$ and using an unusual numeration system we prove that ${\mathcal R}_a$ is homeomorphic to a topological disk.
</p>projecteuclid.org/euclid.ojm/1547607629_20190115220101Tue, 15 Jan 2019 22:01 ESTThe Socle of the Last Term in the Minimal Injective Resolution of a Gorenstein Modulehttps://projecteuclid.org/euclid.ojm/1547607630<strong>Weiling Song</strong>, <strong>Xiaojin Zhang</strong>, <strong>Zhaoyong Huang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 123--132.</p><p><strong>Abstract:</strong><br/>
Let $R$ be a left Noetherian ring, $S$ a right Noetherian ring and $_RU$ a Gorenstein module with $S={\rm End}(_RU)$. If the injective dimensions of $_RU$ and $U_S$ are finite, then the last term in the minimal injective resolution of $_{R}U$ has an essential socle.
</p>projecteuclid.org/euclid.ojm/1547607630_20190115220101Tue, 15 Jan 2019 22:01 ESTFoldings and two-sided tilting complexes for Brauer tree algebrashttps://projecteuclid.org/euclid.ojm/1547607631<strong>Yuta Kozakai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 133--164.</p><p><strong>Abstract:</strong><br/>
In this note, for a Brauer tree algebra $A$ and a star-shaped Brauer tree algebra $B$ which is derived equivalent to $A$, we give operations on the two-sided tilting complex $D_T$ of $A\otimes B^{op}$-modules constructed in [3] which is isomorphic to the Rickard tree-to-star complex $T$ constructed in [5] in $D^b(A)$, and we show that the operations on $D_T$ correspond to operations called $foldings$ on the Rickard tree-to-star complex $T$ given in [7].
</p>projecteuclid.org/euclid.ojm/1547607631_20190115220101Tue, 15 Jan 2019 22:01 ESTUnstabilized weakly reducible Heegaard splittingshttps://projecteuclid.org/euclid.ojm/1547607632<strong>Kun Du</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 165--172.</p><p><strong>Abstract:</strong><br/>
In this paper, we give a sufficient condition for a (weakly reducible) Heegaard splitting to be unstabilized and uncritical. We also give a sufficient condition for a Heegaard splitting to be critical.
</p>projecteuclid.org/euclid.ojm/1547607632_20190115220101Tue, 15 Jan 2019 22:01 ESTPerfect fluid spacetimes with harmonic generalized curvature tensorhttps://projecteuclid.org/euclid.ojm/1547607633<strong>Carlo Alberto Mantica</strong>, <strong>Uday Chand De</strong>, <strong>Young Jin Suh</strong>, <strong>Luca Guido Molinari</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 173--182.</p><p><strong>Abstract:</strong><br/>
We show that $n$-dimensional perfect fluid spacetimes with diver\-gen\-ce-free conformal curvature tensor and constant scalar curvature are generalized Robertson Walker (GRW) spacetimes; as a consequence a perfect fluid Yang pure space is a GRW spacetime. We also prove that perfect fluid spacetimes with harmonic generalized curvature tensor are, under certain conditions, GRW spacetimes. As particular cases, perfect fluids with divergence-free projective, concircular, conharmonic or quasi-conformal curvature tensor are GRW spacetimes. Finally, we explore some physical consequences of such results.
</p>projecteuclid.org/euclid.ojm/1547607633_20190115220101Tue, 15 Jan 2019 22:01 ESTFrobenius structures and characters of affine Lie algebrashttps://projecteuclid.org/euclid.ojm/1547607634<strong>Ikuo Satake</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 183--212.</p><p><strong>Abstract:</strong><br/>
The explicit description of the Frobenius structure for the elliptic root system of type $D_4^{(1,1)}$ in terms of the characters of an affine Lie algebra of type $D_4^{(1)}$ is given.
</p>projecteuclid.org/euclid.ojm/1547607634_20190115220101Tue, 15 Jan 2019 22:01 EST