Kodai Mathematical Journal Articles (Project Euclid)
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The latest articles from Kodai Mathematical Journal 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 EDTThu, 31 Mar 2011 09:07 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Remarks on complete non-compact gradient Ricci expanding solitons
http://projecteuclid.org/euclid.kmj/1278076334
<strong>Li Ma</strong>, <strong>Dezhong Chen</strong><p><strong>Source: </strong>Kodai Math. J., Volume 33, Number 2, 173--181.</p><p><strong>Abstract:</strong><br/> In this paper, we study gradient Ricci expanding solitons ( X,g ) satisfying Rc = cg + D 2 f , where Rc is the Ricci curvature, c < 0 is a constant, and D 2 f is the Hessian of the potential function f on X . We show that for a gradient expanding soliton ( X,g ) with non-negative Ricci curvature, the scalar curvature R has at most one maximum point on X , which is the only minimum point of the potential function f . Furthermore, R > 0 on X unless ( X,g ) is Ricci flat. We also show that there is exponentially decay for scalar curvature on a complete non-compact expanding soliton with its Ricci curvature being ε-pinched. </p>projecteuclid.org/euclid.kmj/1278076334_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTThe Hessian of quantized Ding functionals and its asymptotic behaviorhttps://projecteuclid.org/euclid.kmj/1530496843<strong>Ryosuke Takahashi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 301--314.</p><p><strong>Abstract:</strong><br/>
We compute the Hessian of quantized Ding functionals and give an elementary proof for the convexity of quantized Ding functionals along Bergman geodesics from the view point of projective geometry. We study also the asymptotic behavior of the Hessian using the Berezin-Toeplitz quantization.
</p>projecteuclid.org/euclid.kmj/1530496843_20180701220050Sun, 01 Jul 2018 22:00 EDTCurvature properties of homogeneous real hypersurfaces in nonflat complex space formshttps://projecteuclid.org/euclid.kmj/1530496844<strong>Sadahiro Maeda</strong>, <strong>Hiroshi Tamaru</strong>, <strong>Hiromasa Tanabe</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 315--331.</p><p><strong>Abstract:</strong><br/>
In this paper, we study curvature properties of all homogeneous real hypersurfaces in nonflat complex space forms, and determine their minimalities and the signs of their sectional curvatures completely. These properties reflect the sign of the constant holomorphic sectional curvature $c$ of the ambient space. Among others, for the case of $c$ < 0 there exist homogeneous real hypersurfaces with positive sectional curvature and also ones with negative sectional curvature, whereas for the case of $c$ > 0 there do not exist any homogeneous real hypersurfaces with nonpositive sectional curvature.
</p>projecteuclid.org/euclid.kmj/1530496844_20180701220050Sun, 01 Jul 2018 22:00 EDTOn Perez Del Pozo's lower bound of Weierstrass weighthttps://projecteuclid.org/euclid.kmj/1530496845<strong>Nan Wangyu</strong>, <strong>Masumi Kawasaki</strong>, <strong>Fumio Sakai</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 332--347.</p><p><strong>Abstract:</strong><br/>
Let $V$ be a smooth projective curve over the complex number field with genus $g \geq 2$, and let $\sigma$ be an automorphism on $V$ such that the quotient curve $V/\langle \sigma \rangle$ has genus 0. We write $d$ (resp., $b$) for the order of $\sigma$ (resp., the number of fixed points of $\sigma$). When $d$ and $b$ are fixed, the lower bound of the (Weierstrass) weights of fixed points of $\sigma$ was obtained by Perez del Pozo [7]. We obtain necessary and sufficient conditions for when the lower bound is attained.
</p>projecteuclid.org/euclid.kmj/1530496845_20180701220050Sun, 01 Jul 2018 22:00 EDTConvexity and the Dirichlet problem of translating mean curvature flowshttps://projecteuclid.org/euclid.kmj/1530496846<strong>Li Ma</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 348--358.</p><p><strong>Abstract:</strong><br/>
In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating mean curvature flow is studied and the global existence of the flow and the convergence property are also considered.
</p>projecteuclid.org/euclid.kmj/1530496846_20180701220050Sun, 01 Jul 2018 22:00 EDTOn the complex Łojasiewicz inequality with parameterhttps://projecteuclid.org/euclid.kmj/1530496847<strong>Maciej P. Denkowski</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 359--374.</p><p><strong>Abstract:</strong><br/>
We prove a continuity property in the sense of currents of a continuous family of holomorphic functions which allows us to obtain a Łojasiewicz inequality with an effective exponent independent of the parameter.
</p>projecteuclid.org/euclid.kmj/1530496847_20180701220050Sun, 01 Jul 2018 22:00 EDTBased chord diagrams of spherical curveshttps://projecteuclid.org/euclid.kmj/1530496848<strong>Noboru Ito</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 375--396.</p><p><strong>Abstract:</strong><br/>
This paper demonstrates an approach for developing a framework to produce invariants of base-point-free generic spherical curves under some chosen local moves from Reidemeister moves using based chord diagrams. Our invariants not only contain Arnold's classical generic spherical curve invariant but also new invariants.
</p>projecteuclid.org/euclid.kmj/1530496848_20180701220050Sun, 01 Jul 2018 22:00 EDTFoxby equivalences associated to strongly Gorenstein moduleshttps://projecteuclid.org/euclid.kmj/1530496849<strong>Wanru Zhang</strong>, <strong>Zhongkui Liu</strong>, <strong>Xiaoyan Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 397--412.</p><p><strong>Abstract:</strong><br/>
In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we introduce the notions of strongly $\mathcal{W}_P$-Gorenstein, $\mathcal{W}_I$-Gorenstein and $\mathcal{W}_F$-Gorenstein modules and discuss some basic properties of these modules. We show that the subcategory of strongly Gorenstein projective left $R$-modules in the left Auslander class and the subcategory of strongly $\mathcal{W}_P$-Gorenstein left $S$-modules are equivalent under Foxby equivalence. The injective and flat case are also studied.
</p>projecteuclid.org/euclid.kmj/1530496849_20180701220050Sun, 01 Jul 2018 22:00 EDTOn Terai's conjecturehttps://projecteuclid.org/euclid.kmj/1530496850<strong>Xin Zhang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 413--420.</p><p><strong>Abstract:</strong><br/>
Let $p$ be an odd prime such that $b^r+1=2p^t$, where $r$, $t$ are positive integers and $b \equiv$ 3,5 (mod 8). We show that the Diophantine equation $x^2+b^m=p^n$ has only the positive integer solution $(x,m,n)=(p^t-1,r,2t)$. We also prove that if $b$ is a prime and $r=t=2$, then the above equation has only one solution for the case $b \equiv$ 3,5,7 (mod 8) and the case $d$ is not an odd integer greater than 1 if $b \equiv$ 1 (mod 8), where $d$ is the order of prime divisor of ideal ($p$) in the ideal class group of $\mathbf{Q}$ ($\sqrt {-q}$).
</p>projecteuclid.org/euclid.kmj/1530496850_20180701220050Sun, 01 Jul 2018 22:00 EDTThe effect of Fenchel-Nielsen coordinates under elementary moveshttps://projecteuclid.org/euclid.kmj/1530496851<strong>Dong Tan</strong>, <strong>Peijia Liu</strong>, <strong>Xuewen Liu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 421--439.</p><p><strong>Abstract:</strong><br/>
We describe the effect of Fenchel-Nielsen coordinates under elementary move for hyperbolic surfaces with geodesic boundaries, punctures and cone points, which generalize Okai's result for surfaces with geodesic boundaries. The proof relies on the parametrization of the Teichmüller space of surface of type (1,1) or (0,4) as a sub-locus of an algebraic equation in $\mathbf{R}^3$. As an application, we show that the hyperbolic length functions of closed curves are asymptotically piecewise linear functions with respect to the Fenchel Nielsen coordinates in the Teichmüller spaces of surfaces with cone points.
</p>projecteuclid.org/euclid.kmj/1530496851_20180701220050Sun, 01 Jul 2018 22:00 EDTA prime geodesic theorem for higher rank buildingshttps://projecteuclid.org/euclid.kmj/1530496852<strong>Anton Deitmar</strong>, <strong>Rupert McCallum</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 440--455.</p><p><strong>Abstract:</strong><br/>
We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.
</p>projecteuclid.org/euclid.kmj/1530496852_20180701220050Sun, 01 Jul 2018 22:00 EDTA note on families of monogenic number fieldshttps://projecteuclid.org/euclid.kmj/1530496853<strong>Joachim König</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 456--464.</p><p><strong>Abstract:</strong><br/>
We give a sufficient criterion for specializations of certain families of polynomials to yield monogenic number fields. This generalizes constructions in several earlier papers. As applications we give new infinite families of monogenic number fields for several prescribed Galois groups.
</p>projecteuclid.org/euclid.kmj/1530496853_20180701220050Sun, 01 Jul 2018 22:00 EDTEnergy gaps for $p$-Yang-Mills fields over compact Riemannian manifoldshttps://projecteuclid.org/euclid.kmj/1540951247<strong>Zhen-Rong Zhou</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 465--474.</p><p><strong>Abstract:</strong><br/>
In this paper, an inequality of Simons type for $p$-Yang-Mills fields is established over compact Riemannian manifolds, and then, the energy gaps are obtained.
</p>projecteuclid.org/euclid.kmj/1540951247_20181030220129Tue, 30 Oct 2018 22:01 EDTA new formula for the spherical growth series of an amalgamated free product of two infinite cyclic groupshttps://projecteuclid.org/euclid.kmj/1540951250<strong>Michihiko Fujii</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 475--511.</p><p><strong>Abstract:</strong><br/>
We consider a group presented as $G(p,q) = \langle x, y|x^p = y^q\rangle$, with integers $p$ and $q$ satisfying $2 \leq p \leq q$. The group is an amalgamated free product of two infinite cyclic groups and is geometrically realized as the fundamental group of a Seifert fiber space over the 2-dimensional disk with two cone points whose associated cone angles are $\frac{2\pi}{p}$ and $\frac{2\pi}{q}$. We present a formula for the spherical growth series of the group $G(p,q)$ with respect to the generating set $\{x,y,x^{-1}, y^{-1}\}$, from which a rational function expression for the spherical growth series of $G(p,q)$ is derived concretely, once $p$ and $q$ are given. In fact, an elementary computer program constructed from the formula yields an explicit form of a single rational fraction expression for the spherical growth series of $G(p,q)$. Such expressions for several pairs $(p,q)$ appear in this paper. In 1999, C. P. Gill already provided a similar formula for the same group. The formula given here takes a different form from his formula, because the method we used here is independent of that introduced by him.
</p>projecteuclid.org/euclid.kmj/1540951250_20181030220129Tue, 30 Oct 2018 22:01 EDT$q$-series reciprocities and further $\pi$-formulaehttps://projecteuclid.org/euclid.kmj/1540951251<strong>Wenchang Chu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 512--530.</p><p><strong>Abstract:</strong><br/>
By examining reciprocal relations of basic well-poised, quadratic and cubic series, we establish $q$-analogues of three infinite series for $1/\pi^2$ due to Guillera (2003) and $\lambda$-parameter extensions of three infinite series for $1/\pi$ due to Ramanujan (1914). Several further infinite series identities of Ramanujan-type are also derived as consequences.
</p>projecteuclid.org/euclid.kmj/1540951251_20181030220129Tue, 30 Oct 2018 22:01 EDTArea of the complement of the fast escaping sets of a family of entire functionshttps://projecteuclid.org/euclid.kmj/1540951252<strong>Song Zhang</strong>, <strong>Fei Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 531--553.</p><p><strong>Abstract:</strong><br/>
Let $f$ be an entire function with the form $f(z)=P(e^z)/e^z$, where $P$ is a polynomial with $\deg(P)\geq2$ and $P(0)\neq 0$. We prove that the area of the complement of the fast escaping set (hence the Fatou set) of $f$ in a horizontal strip of width $2\pi$ is finite. In particular, the corresponding result can be applied to the sine family $\alpha\sin(z+\beta)$, where $\alpha\neq 0$ and $\beta\in\mathbf{C}$.
</p>projecteuclid.org/euclid.kmj/1540951252_20181030220129Tue, 30 Oct 2018 22:01 EDTHigher Bers maps and Weil-Petersson Teichm\"uller spacehttps://projecteuclid.org/euclid.kmj/1540951253<strong>Shuan Tang</strong>, <strong>Jianjun Jin</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 554--565.</p><p><strong>Abstract:</strong><br/>
It is known that the Bers map, induced by Schwarzian derivative differential operator, is a holomorphic split submersion in Weil-Petersson Teichmüller space. We prove that the higher Bers maps which induced by some higher Schwarzian differential operators in Weil-Petersson Teichmüller space are holomorphic and its differentials at the origin are bounded and surjective.
</p>projecteuclid.org/euclid.kmj/1540951253_20181030220129Tue, 30 Oct 2018 22:01 EDTVojta's conjecture, singularities and multiplier-type idealshttps://projecteuclid.org/euclid.kmj/1540951254<strong>Takehiko Yasuda</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 566--578.</p><p><strong>Abstract:</strong><br/>
We formulate a generalization of Vojta's conjecture in terms of log pairs and variants of multiplier ideals.
</p>projecteuclid.org/euclid.kmj/1540951254_20181030220129Tue, 30 Oct 2018 22:01 EDTDerived category with respect to Gorenstein AC-projective moduleshttps://projecteuclid.org/euclid.kmj/1540951255<strong>Tianya Cao</strong>, <strong>Zhongkui Liu</strong>, <strong>Xiaoyan Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 579--590.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to study the derived category with respect to Gorenstein AC-projective modules. We characterize the bounded Gorenstein AC derived category and obtain some triangle equivalences. We also establish a right recollement related with Gorenstein AC derived category.
</p>projecteuclid.org/euclid.kmj/1540951255_20181030220129Tue, 30 Oct 2018 22:01 EDTOn cobrackets on the Wilson loops associated with flat $\mathrm{GL}(1, \mathbf{R})$-bundles over surfaceshttps://projecteuclid.org/euclid.kmj/1540951256<strong>Moeka Nobuta</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 591--619.</p><p><strong>Abstract:</strong><br/>
Let $S$ be a closed connected oriented surface of genus $g>0$. We study a Poisson subalgebra $W_1(g)$ of $C^{\infty}(\mathrm{Hom}(\pi_1(S), \mathrm{GL}(1, \mathbf{R}))/\mathrm{GL}(1, \mathbf{R}))$, the smooth functions on the moduli space of flat $\mathrm{GL}(1, \mathbf{R})$-bundles over $S$. There is a surjective Lie algebra homomorphism from the Goldman Lie algebra onto $W_1(g)$. We classify all cobrackets on $W_1(g)$ up to coboundary, that is, we compute $H^1(W_1(g), W_1(g) \wedge W_1(g)) \cong \mathrm{Hom}(\mathbf{Z}^{2g}, \mathbf{R})$. As a result, there is no cohomology class corresponding to the Turaev cobracket on $W_1(g)$.
</p>projecteuclid.org/euclid.kmj/1540951256_20181030220129Tue, 30 Oct 2018 22:01 EDT{\L}ojasiewicz exponents of non-degenerate holomorohic and mixed functionshttps://projecteuclid.org/euclid.kmj/1540951257<strong>Mutsuo Oka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 620--651.</p><p><strong>Abstract:</strong><br/>
We consider {\L}ojasiewicz inequalities for a non-degenerate holomorphic function with an isolated singularity at the origin. We give an explicit estimation of the {\L}ojasiewicz exponent in a slightly weaker form than the assertion in Fukui [10]. We also introduce {\L}ojasiewicz inequality for strongly non-degenerate mixed functions and generalize this estimation for mixed functions.
</p>projecteuclid.org/euclid.kmj/1540951257_20181030220129Tue, 30 Oct 2018 22:01 EDTZariskian adic spaceshttps://projecteuclid.org/euclid.kmj/1540951258<strong>Hiromu Tanaka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 652--695.</p><p><strong>Abstract:</strong><br/>
We introduce a Zariskian analogue of the theory of Huber's adic spaces.
</p>projecteuclid.org/euclid.kmj/1540951258_20181030220129Tue, 30 Oct 2018 22:01 EDTOn the supersingular divisors of nilpotent admissible indigenous bundleshttps://projecteuclid.org/euclid.kmj/1552982501<strong>Yuichiro Hoshi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 1--47.</p><p><strong>Abstract:</strong><br/>
In the present paper, we give a characterization of the supersingular divisors [i.e., the zero loci of the Hasse invariants] of nilpotent admissible/ordinary indigenous bundles on hyperbolic curves. By applying the characterization, we also obtain lists of the nilpotent indigenous bundles on certain hyperbolic curves. Moreover, we prove the hyperbolic ordinariness of certain hyperbolic curves.
</p>projecteuclid.org/euclid.kmj/1552982501_20190319040205Tue, 19 Mar 2019 04:02 EDTBiharmonic orbits of isotropy representations of symmetric spaceshttps://projecteuclid.org/euclid.kmj/1552982505<strong>Shinji Ohno</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 48--63.</p><p><strong>Abstract:</strong><br/>
In this paper, we give a necessarly and sufficient condition for orbits of linear isotropy representations of Riemannian symmetric spaces are biharmonic submanifolds in hyperspheres in Euclidean spaces. In particular, we obtain examples of biharmonic submanifolds in hyperspheres whose co-dimension is greater than one.
</p>projecteuclid.org/euclid.kmj/1552982505_20190319040205Tue, 19 Mar 2019 04:02 EDTSome remarks on Riemannian manifolds with parallel Cotton tensorhttps://projecteuclid.org/euclid.kmj/1552982506<strong>Hai-Ping Fu</strong>, <strong>Gao-Bo Xu</strong>, <strong>Yong-Qian Tao</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 64--74.</p><p><strong>Abstract:</strong><br/>
We give some sufficient conditions for stochastically complete Riemannian manifolds with parallel Cotton tensor to be either Einstein or of constant sectional curvature, and obtain an optimal pinching theorem. In particular, when $n$ = 4, we give a full classification.
</p>projecteuclid.org/euclid.kmj/1552982506_20190319040205Tue, 19 Mar 2019 04:02 EDTZariski-van Kampen theorems for singular varieties—an approach via the relative monodromy variationhttps://projecteuclid.org/euclid.kmj/1552982507<strong>Christophe Eyral</strong>, <strong>Peter Petrov</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 75--98.</p><p><strong>Abstract:</strong><br/>
The classical Zariski-van Kampen theorem gives a presentation of the fundamental group of the complement of a complex algebraic curve in $\mathbf{P}^2$. The first generalization of this theorem to singular (quasi-projective) varieties was given by the first author. In both cases, the relations are generated by the standard monodromy variation operators associated with the special members of a generic pencil of hyperplane sections. In the present paper, we give a new generalization in which the relations are generated by the \emph{relative} monodromy variation operators introduced by D. Chéniot and the first author. The advantage of using the relative operators is not only to cover a larger class of varieties but also to unify the Zariski-van Kampen type theorems for the fundamental group and for higher homotopy groups. In the special case of non-singular varieties, the main result of this paper was conjectured by D. Chéniot and the first author.
</p>projecteuclid.org/euclid.kmj/1552982507_20190319040205Tue, 19 Mar 2019 04:02 EDTNote on class number parity of an abelian field of prime conductor, IIhttps://projecteuclid.org/euclid.kmj/1552982508<strong>Humio Ichimura</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 99--110.</p><p><strong>Abstract:</strong><br/>
For a fixed integer $n \geq 1$, let $p=2n\ell+1$ be a prime number with an odd prime number $\ell$, and let $F=F_{p,\ell}$ be the real abelian field of conductor $p$ and degree $\ell$. We show that the class number $h_F$ of $F$ is odd when 2 remains prime in the real $\ell$th cyclotomic field $\mathbf{Q}(\zeta_{\ell})^+$ and $\ell$ is sufficiently large.
</p>projecteuclid.org/euclid.kmj/1552982508_20190319040205Tue, 19 Mar 2019 04:02 EDTde Rham theory and cocycles of cubical sets from smooth quandleshttps://projecteuclid.org/euclid.kmj/1552982509<strong>Takefumi Nosaka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 111--129.</p><p><strong>Abstract:</strong><br/>
We show a de Rham theorem for cubical manifolds, and study rational homotopy type of the classifying spaces of smooth quandles. We also show that secondary characteristic classes in [8, 9] produce cocycles of quandles.
</p>projecteuclid.org/euclid.kmj/1552982509_20190319040205Tue, 19 Mar 2019 04:02 EDTThe gamma filtrations of $K$-theory of complete flag varietieshttps://projecteuclid.org/euclid.kmj/1552982510<strong>Nobuaki Yagita</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 130--159.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a compact Lie group and $T$ its maximal torus. In this paper, we try to compute $gr_{\gamma}^*(G/T)$ the graded ring associated with the gamma filtration of the complex $K$-theory $K^0(G/T)$. We use the Chow rings of corresponding versal flag varieties.
</p>projecteuclid.org/euclid.kmj/1552982510_20190319040205Tue, 19 Mar 2019 04:02 EDTConformal and projective characterizations of an odd dimensional unit spherehttps://projecteuclid.org/euclid.kmj/1552982511<strong>Ramesh Sharma</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 160--169.</p><p><strong>Abstract:</strong><br/>
We obtain two characterizations of an odd-dimensional unit sphere of dimension $>3$ by proving the following two results: (i) If a complete connected $\eta$-Einstein $K$-contact manifold $M$ of dimension $>3$ admits a conformal vector field $V$, then either $M$ is isometric to a unit sphere, or $V$ is an infinitesimal automorphism of $M$. (ii) If $V$ was a projective vector field in (i), then the same conclusions would hold, except in the first case, $M$ would be locally isometric to a unit sphere.
</p>projecteuclid.org/euclid.kmj/1552982511_20190319040205Tue, 19 Mar 2019 04:02 EDTOn the Chow groups of certain EPW sexticshttps://projecteuclid.org/euclid.kmj/1552982512<strong>Robert Laterveer</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 170--201.</p><p><strong>Abstract:</strong><br/>
This note is about the Hilbert square $X=S^{[2]}$, where $S$ is a general $K3$ surface of degree 10, and the anti-symplectic birational involution $\iota$ of $X$ constructed by O'Grady. The main result is that the action of $\iota$ on certain pieces of the Chow groups of $X$ is as expected by Bloch's conjecture. Since $X$ is birational to a double EPW sextic $X^\prime$, this has consequences for the Chow ring of the EPW sextic $Y\subset\mathbf{P}^5$ associated to $X^\prime$.
</p>projecteuclid.org/euclid.kmj/1552982512_20190319040205Tue, 19 Mar 2019 04:02 EDTRelationships among non-flat totally geodesic surfaces in symmetric spaces of type A and their polynomial representationshttps://projecteuclid.org/euclid.kmj/1562032828<strong>Hideya Hashimoto</strong>, <strong>Misa Ohashi</strong>, <strong>Kazuhiro Suzuki</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 203--222.</p><p><strong>Abstract:</strong><br/>
We give computational systems of polynomial representations of the composition maps of non-flat totally geodesic surfaces of the symmetric spaces of type A which are obtained by K. Mashimo, and the Cartan imbeddings of symmetric spaces of type A to $SU(n)$. We obtain the relationships among the non-flat totally geodesic surfaces in symmetric spaces of types AI, AII and AIII by this methods.
</p>projecteuclid.org/euclid.kmj/1562032828_20190701220109Mon, 01 Jul 2019 22:01 EDTSome examples of global Poisson structures on $S^4$https://projecteuclid.org/euclid.kmj/1562032829<strong>Takayuki Moriyama</strong>, <strong>Takashi Nitta</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 223--246.</p><p><strong>Abstract:</strong><br/>
A Poisson structure is a bivector whose Schouten bracket vanishes. We study a global Poisson structure on $S^4$ associated with a holomorphic Poisson structure on $\mathbf{CP}^3$. The space of such Poisson structures on $S^4$ is realised as a real algebraic variety in the space of holomorphic Poisson structures on $\mathbf{CP}^3$. We generalize the result to the higher dimensional case $\mathbf{HP}^n$ by the twistor method. It is known that a holomorphic Poisson structure on $\mathbf{CP}^3$ corresponds to a codimension one holomorphic foliation and the space of these foliations of degree 2 has six components. In this paper we provide examples of Poisson structures on $S^4$ associated with these components.
</p>projecteuclid.org/euclid.kmj/1562032829_20190701220109Mon, 01 Jul 2019 22:01 EDTOn scaling limit of a cost in adhoc network modelhttps://projecteuclid.org/euclid.kmj/1562032830<strong>Yukio Nagahata</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 247--273.</p><p><strong>Abstract:</strong><br/>
We are interested in giving a mathematical formula of a cost in adhoc network model. In our model, the cost is formulated as an application of first-passage percolation and the motion of devices is random, and an asymptotic density of devices is formulated by hydrodynamic limit. Under some technical assumptions, we give asymptotics of a cost in adhoc network model. In order to formulate this model, we extend the results of first-passage percolation given by Howard Newman [3] to that in inhomogeneous environments.
</p>projecteuclid.org/euclid.kmj/1562032830_20190701220109Mon, 01 Jul 2019 22:01 EDTThick representations and dense representations Ihttps://projecteuclid.org/euclid.kmj/1562032831<strong>Kazunori Nakamoto</strong>, <strong>Yasuhiro Omoda</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 274--307.</p><p><strong>Abstract:</strong><br/>
We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute denseness are open conditions for representations. Thereby, we can construct the moduli schemes of absolutely thick representations and absolutely dense representations. We also describe several results and several examples on thick representations for developing a theory of thick representations.
</p>projecteuclid.org/euclid.kmj/1562032831_20190701220109Mon, 01 Jul 2019 22:01 EDTAutomorphism groups of smooth plane curveshttps://projecteuclid.org/euclid.kmj/1562032832<strong>Takeshi Harui</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 308--331.</p><p><strong>Abstract:</strong><br/>
The author classifies finite groups acting on smooth plane curves of degree at least four. Furthermore, he gives an upper bound for the order of automorphism groups of smooth plane curves and determines the exceptional cases in terms of defining equations. This paper also contains a simple proof of the uniqueness of smooth plane curves with the full automorphism group of maximum order for each degree.
</p>projecteuclid.org/euclid.kmj/1562032832_20190701220109Mon, 01 Jul 2019 22:01 EDTAn infinite sequence of ideal hyperbolic Coxeter 4-polytopes and Perron numbershttps://projecteuclid.org/euclid.kmj/1562032833<strong>Tomoshige Yukita</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 332--357.</p><p><strong>Abstract:</strong><br/>
In [7], Kellerhals and Perren conjectured that the growth rates of cocompact hyperbolic Coxeter groups are Perron numbers. By results of Floyd, Parry, Kolpakov, Nonaka-Kellerhals, Komori and the author [1], [3], [8], [10], [12], [13], [21], [22], the growth rates of 2- and 3-dimensional hyperbolic Coxeter groups are always Perron numbers. Kolpakov and Talambutsa showed that the growth rates of right-angled Coxeter groups are Perron numbers [9]. For certain families of 4-dimensional cocompact hyperbolic Coxeter groups, the conjecture holds as well (see [7], [19] and also [23]). In this paper, we construct an infinite sequence of ideal non-simple hyperbolic Coxeter 4-polytopes giving rise to growth rates which are distinct Perron numbers. This is the first explicit example of an infinite family of non-compact finite volume Coxeter polytopes in hyperbolic 4-space whose growth rates are of the conjectured arithmetic nature as well.
</p>projecteuclid.org/euclid.kmj/1562032833_20190701220109Mon, 01 Jul 2019 22:01 EDTA Cesàro average of generalised Hardy-Littlewood numbershttps://projecteuclid.org/euclid.kmj/1562032834<strong>Alessandro Languasco</strong>, <strong>Alessandro Zaccagnini</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 358--375.</p><p><strong>Abstract:</strong><br/>
We continue our recent work on additive problems with prime summands: we already studied the average number of representations of an integer as a sum of two primes, and also considered individual integers. Furthermore, we dealt with representations of integers as sums of powers of prime numbers. In this paper, we study a Cesàro weighted partial explicit formula for generalised Hardy-Littlewood numbers (integers that can be written as a sum of a prime power and a square) thus extending and improving our earlier results.
</p>projecteuclid.org/euclid.kmj/1562032834_20190701220109Mon, 01 Jul 2019 22:01 EDTThe isometric embedding of the augmented Teichmüller space of a Riemann surface into the augmented Teichmüller space of its covering surfacehttps://projecteuclid.org/euclid.kmj/1562032835<strong>Guangming Hu</strong>, <strong>Yi Qi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 376--392.</p><p><strong>Abstract:</strong><br/>
It is known that every finitely unbranched holomorphic covering $\pi:\widetilde{S}\rightarrow S$ of a compact Riemann surface $S$ with genus $g\geq2$ induces an isometric embedding $\Phi_{\pi} :Teich(S)\rightarrow Teich(\widetilde{S})$. By the mutual relations between Strebel rays in $Teich(S)$ and their embeddings in $Teich(\widetilde{S})$, we show that the augmented Teichmüller space $\widehat{Teich}(S)$ can be isometrically embedded in the augmented Teichmüller space $\widehat{Teich}(\widetilde{S})$.
</p>projecteuclid.org/euclid.kmj/1562032835_20190701220109Mon, 01 Jul 2019 22:01 EDTA p -analogue of the multiple Euler constanthttps://projecteuclid.org/euclid.kmj/1562032836<strong>Nobushige Kurokawa</strong>, <strong>Yuichiro Taguchi</strong>, <strong>Hidekazu Tanaka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 2, 393--408.</p><p><strong>Abstract:</strong><br/>
We study a p -analogue of the multiple Euler constant. Then we show that it can be described by the congruence zeta function attached to powers of G m over F p . Moreover, we show that it converges to the multiple Euler constant as p → 1.
</p>projecteuclid.org/euclid.kmj/1562032836_20190701220109Mon, 01 Jul 2019 22:01 EDTFamilies of $K3$ surfaces and curves of (2,3)-torus typehttps://projecteuclid.org/euclid.kmj/1572487224<strong>Makiko Mase</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 409--430.</p><p><strong>Abstract:</strong><br/>
We study families of $K3$ surfaces obtained by double covering of the projective plane branching along curves of (2,3)-torus type. In the first part, we study the Picard lattices of the families, and a lattice duality of them. In the second part, we describe a deformation of singularities of Gorenstein $K3$ surfaces in these families.
</p>projecteuclid.org/euclid.kmj/1572487224_20191030220055Wed, 30 Oct 2019 22:00 EDTNéron models of 1-motives and dualityhttps://projecteuclid.org/euclid.kmj/1572487228<strong>Takashi Suzuki</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 431--475.</p><p><strong>Abstract:</strong><br/>
In this paper, we propose a definition of Néron models of arbitrary Deligne 1-motives over Dedekind schemes, extending Néron models of semi-abelian varieties. The key property of our Néron models is that they satisfy a generalization of Grothendieck's duality conjecture in SGA 7 when the residue fields of the base scheme at closed points are perfect. The assumption on the residue fields is unnecessary for the class of 1-motives with semistable reduction everywhere. In general, this duality holds after inverting the residual characteristics. The definition of Néron models involves careful treatment of ramification of lattice parts and its interaction with semi-abelian parts. This work is a complement to Grothendieck's philosophy on Néron models of motives of arbitrary weights.
</p>projecteuclid.org/euclid.kmj/1572487228_20191030220055Wed, 30 Oct 2019 22:00 EDTOn the family of Riemann surfaces with tetrahedral group actionhttps://projecteuclid.org/euclid.kmj/1572487229<strong>Ryota Hirakawa</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 476--495.</p><p><strong>Abstract:</strong><br/>
This is the second of our series of papers to solve Mutsuo Oka's problems concerning our polyhedral construction of degenerations of Riemann surfaces. Oka posed globalization problem of our degenerations and determination problem of the defining equation of a Riemann surface appearing in our construction—which is equipped with the standard tetrahedral group action (i.e. topologically equivalent to the tetrahedral group action on the cable surface of the tetrahedron). A joint work with S. Takamura solved the first problem. In this paper, we solve the second one—in an unexpected way: an algebraic curve with the standard tetrahedral group action turns out to be not unique: a sporadic one (hyperelliptic) and a 1-parameter family of non-hyperelliptic curves. We study their properties. At first glance they are `independent', but actually intricately connected—we show that at one special value in this family, a degeneration whose monodromy is a hyperelliptic involution occurs, and the sporadic hyperelliptic curve emerges after the stable reduction ( hyperelliptic jump ). This jumping phenomenon seems deeply related to the moduli geometry and is possibly universal for other families of curves with finite group actions. Based on this observation, we pose stably-connectedness problem .
</p>projecteuclid.org/euclid.kmj/1572487229_20191030220055Wed, 30 Oct 2019 22:00 EDTGeometric invariants of 5/2-cuspidal edgeshttps://projecteuclid.org/euclid.kmj/1572487230<strong>Atsufumi Honda</strong>, <strong>Kentaro Saji</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 496--525.</p><p><strong>Abstract:</strong><br/>
We introduce two invariants called the secondary cuspidal curvature and the bias on 5/2-cuspidal edges, and investigate their basic properties. While the secondary cuspidal curvature is an analog of the cuspidal curvature of (ordinary) cuspidal edges, there are no invariants corresponding to the bias. We prove that the product (called the secondary product curvature ) of the secondary cuspidal curvature and the limiting normal curvature is an intrinsic invariant. Using this intrinsicity, we show that any real analytic 5/2-cuspidal edges with non-vanishing limiting normal curvature admit non-trivial isometric deformations, which provides the extrinsicity of various invariants.
</p>projecteuclid.org/euclid.kmj/1572487230_20191030220055Wed, 30 Oct 2019 22:00 EDTOn a rigidity of some modular Galois deformationshttps://projecteuclid.org/euclid.kmj/1572487231<strong>Yuichi Shimada</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 526--565.</p><p><strong>Abstract:</strong><br/>
Let $F$ be a totally real field and $\mathbf{\rho} = (\rho_{\lambda})_{\lambda}$ be a compatible system of two dimensional $\lambda$-adic representations of the Galois group of $F$. We assume that $\mathbf{\rho}$ has a residually modular $\lambda$-adic realization for some $\lambda$. In this paper, we consider local behaviors of modular deformations of $\lambda$-adic realizations of $\mathbf{\rho}$ at unramified primes. In order to control local deformations at specified unramified primes, we construct certain Hecke modules. Applying Kisin's Taylor-Wiles system, we obtain an $R = T$ type result supplemented with local conditions at specified unramified primes. As a consequence, we shall show a potential rigidity of some modular deformations of infinitely many $\lambda$-adic realizations of $\mathbf{\rho}$.
</p>projecteuclid.org/euclid.kmj/1572487231_20191030220055Wed, 30 Oct 2019 22:00 EDTA weak coherence theorem and remarks to the Oka theoryhttps://projecteuclid.org/euclid.kmj/1572487232<strong>Junjiro Noguchi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 566--586.</p><p><strong>Abstract:</strong><br/>
The proofs of K. Oka's Coherence Theorems are based on Weierstrass' Preparation (division) Theorem. Here we formulate and prove a Weak Coherence Theorem without using Weierstrass' Preparation Theorem, but only with power series expansions : The proof is almost of linear algebra. Nevertheless, this simple Weak Coherence Theorem suffices to give other proofs of the Approximation, Cousin I/II, and Levi's (Hartogs' Inverse) Problems even in simpler ways than those known, as far as the domains are non-singular; they constitute the main basic part of the theory of several complex variables.
The new approach enables us to complete the proofs of those problems in quite an elementary way without Weierstrass' Preparation Theorem or the cohomology theory of Cartan-Serre, nor $L^2$-${\bar{\partial}}$ method of Hörmander.
We will also recall some new historical facts that Levi's (Hartogs' Inverse) Problem of general dimension $n \geq 2$ was, in fact, solved by K. Oka in 1943 (unpublished) and by S. Hitotsumatsu in 1949 (published in Japanese), whereas it has been usually recognized as proved by K. Oka 1953, by H. J. Bremermann and by F. Norguet 1954, independently.
</p>projecteuclid.org/euclid.kmj/1572487232_20191030220055Wed, 30 Oct 2019 22:00 EDTA topological characterization of the strong disk property on open Riemann surfaceshttps://projecteuclid.org/euclid.kmj/1572487233<strong>Makoto Abe</strong>, <strong>Gou Nakamura</strong>, <strong>Hiroshige Shiga</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 587--592.</p><p><strong>Abstract:</strong><br/>
In this paper, we give a topological characterization of a subdomain $G$ of an open Riemann surface $R$ which has the strong disk property. Namely, we show that the domain $G$ satisfies the strong disk property in $R$ if and only if the canonical homomorphism $\pi_1(G) \to \pi_1(R)$ is injective.
</p>projecteuclid.org/euclid.kmj/1572487233_20191030220055Wed, 30 Oct 2019 22:00 EDTOn the number of cusps of perturbations of complex polynomialshttps://projecteuclid.org/euclid.kmj/1572487234<strong>Kazumasa Inaba</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 593--610.</p><p><strong>Abstract:</strong><br/>
Let $f$ be a 1-variable complex polynomial such that $f$ has an isolated singularity at the origin. In the present paper, we show that there exists a perturbation $f_{t}$ of $f$ which has only fold singularities and cusps as singularities of a real polynomial map from $\mathbf{R}^2$ to $\mathbf{R}^2$. We then calculate the number of cusps of $f_t$ in a sufficiently small neighborhood of the origin and estimate the number of cusps of $f_t$ in $\mathbf{R}^2$.
</p>projecteuclid.org/euclid.kmj/1572487234_20191030220055Wed, 30 Oct 2019 22:00 EDTBifurcation from infinity for a quasilinear equation with general nonlinearityhttps://projecteuclid.org/euclid.kmj/1572487235<strong>Ohsang Kwon</strong>, <strong>Youngae Lee</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 3, 611--632.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a nonautonomous quasilinear equation with general nonlinearity. Our main goal is to show the existence and asymptotic behavior of solutions with small parameter, which correponds to the bifurcation from infinity.
</p>projecteuclid.org/euclid.kmj/1572487235_20191030220055Wed, 30 Oct 2019 22:00 EDTMutation invariance for the zeroth coefficients of colored HOMFLY polynomialhttps://projecteuclid.org/euclid.kmj/1584345685<strong>Tetsuya Ito</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
We show that the zeroth coefficient of the cables of the HOMFLY polynomial (colored HOMFLY polynomials) does not distinguish mutants. This makes a sharp contrast with the total HOMFLY polynomial whose 3-cables can distinguish mutants.
</p>projecteuclid.org/euclid.kmj/1584345685_20200316040132Mon, 16 Mar 2020 04:01 EDTGradient estimates of a general porous medium equation for the V-Laplacianhttps://projecteuclid.org/euclid.kmj/1584345686<strong>Hongbing Qiu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 16--41.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider the gradient estimates for the positive solutions to the following porous medium equation
$u_t = \Delta_V u^m$,
where $m>1$. We obtain Li-Yau type bounds of the above equation on Riemannian manifolds with Bakry-Emery type curvature bounded from below, which improves the estimates in [25] and covers the ones in [22, 18, 19, 27].
</p>projecteuclid.org/euclid.kmj/1584345686_20200316040132Mon, 16 Mar 2020 04:01 EDT$r$-Almost Newton-Ricci solitons immersed in a Lorentzian manifold: examples, nonexistence and rigidityhttps://projecteuclid.org/euclid.kmj/1584345687<strong>Antonio W. Cunha</strong>, <strong>Eudes L. de Lima</strong>, <strong>Henrique F. de Lima</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 42--56.</p><p><strong>Abstract:</strong><br/>
We establish the concept of $r$-almost Newton-Ricci soliton immersed into a Lorentzian manifold, which extends in a natural way the almost Ricci solitons introduced by Pigola, Rigoli, Rimoldi and Setti in [17]. In this setting, under suitable hypothesis on the potential and soliton functions, we obtain nonexistence and rigidity results. Some interesting examples of these new geometric objects are also given.
</p>projecteuclid.org/euclid.kmj/1584345687_20200316040132Mon, 16 Mar 2020 04:01 EDTGeometric polarized log Hodge structures with a base of log rank onehttps://projecteuclid.org/euclid.kmj/1584345688<strong>Taro Fujisawa</strong>, <strong>Chikara Nakayama</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 57--83.</p><p><strong>Abstract:</strong><br/>
We prove that a projective vertical exact log smooth morphism of fs log analytic spaces with a base of log rank one yields polarized log Hodge structures in the canonical way.
</p>projecteuclid.org/euclid.kmj/1584345688_20200316040132Mon, 16 Mar 2020 04:01 EDTHeat kernel asymptotics on sequences of elliptically degenerating Riemann surfaceshttps://projecteuclid.org/euclid.kmj/1584345689<strong>Daniel Garbin</strong>, <strong>Jay Jorgenson</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 84--128.</p><p><strong>Abstract:</strong><br/>
This is the first of two articles in which we define an elliptically degenerating family of hyperbolic Riemann surfaces and study the asymptotic behavior of the associated spectral theory. Our study is motivated by a result which Hejhal attributes to Selberg, proving spectral accumulation for the family of Hecke triangle groups. In this article, we prove various results regarding the asymptotic behavior of heat kernels and traces of heat kernels for both real and complex time. In Garbin et al. (2018) [8], we will use the results from this article and study the asymptotic behavior of numerous spectral functions through elliptic degeneration, including spectral counting functions, Selberg's zeta function, Hurwitz-type zeta functions, determinants of the Laplacian, wave kernels, spectral projections, small eigenfunctions, and small eigenvalues. The method of proof we employ follows the template set in previous articles which study spectral theory on degenerating families of finite volume Riemann surfaces (Huntley et al. (1995) [14] and (1997) [15], Jorgenson et al. (1997) [20] and (1997) [17]) and on degenerating families of finite volume hyperbolic three manifolds (Dodziuk et al. (1998) [4].) Although the types of results developed here and in Garbin et al. (2018) [8], are similar to those in existing articles, it is necessary to thoroughly present all details in the setting of elliptic degeneration in order to uncover all nuances in this setting.
</p>projecteuclid.org/euclid.kmj/1584345689_20200316040132Mon, 16 Mar 2020 04:01 EDTOn the rank of elliptic curves arising from Pythagorean quadrupletshttps://projecteuclid.org/euclid.kmj/1584345690<strong>Arman Shamsi Zargar</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 129--142.</p><p><strong>Abstract:</strong><br/>
By a Pythagorean quadruplet $(a,b,c,d)$, we mean an integer solution to the quadratic equation $a^2 + b^2 = c^2 + d^2$. We use this notion to construct infinite families of elliptic curves of higher rank as far as possible. Furthermore, we give particular examples of rank eight.
</p>projecteuclid.org/euclid.kmj/1584345690_20200316040132Mon, 16 Mar 2020 04:01 EDTMonotonicity of eigenvalues of the $p$-Laplace operator under the Ricci-Bourguignon flowhttps://projecteuclid.org/euclid.kmj/1584345691<strong>Ha Tuan Dung</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 143--161.</p><p><strong>Abstract:</strong><br/>
Given a compact Riemannian manifold without boundary, in this paper, we discuss the monotonicity of the first eigenvalue of the $p$-Laplace operator under the Ricci-Bourguignon flow. We prove that the first eigenvalue of the $p$-Laplace operator is strictly monotone increasing and differentiable almost everywhere along the Ricci-Bourguignon flow under some different curvature assumptions. Moreover, we obtain various monotonicity quantities about the first eigenvalue of the $p$-Laplace operator along the Ricci-Bourguignon flow.
</p>projecteuclid.org/euclid.kmj/1584345691_20200316040132Mon, 16 Mar 2020 04:01 EDTA note on the extendability of holomorphic motionshttps://projecteuclid.org/euclid.kmj/1584345692<strong>Hiroshige Shiga</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 162--169.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider conditions under which a holomorphic motion of a closed subset of Ĉ over a non-simply connected Riemann surface $X$ can be extended to a holomorphic motion of Ĉ over $X$. We construct examples of non-extendable holomorphic motions which satisfy fairy good topological conditions. The examples are also counter-examples to a claim by Chirka for the extendability of holomorphic motions.
</p>projecteuclid.org/euclid.kmj/1584345692_20200316040132Mon, 16 Mar 2020 04:01 EDTLagrangian submanifolds of $S^6$ and the associative Grassmann manifoldhttps://projecteuclid.org/euclid.kmj/1584345693<strong>Kanako Enoyoshi</strong>, <strong>Kazumi Tsukada</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 170--192.</p><p><strong>Abstract:</strong><br/>
We focus on Lagrangian submanifolds of a six-dimensional sphere in the space Im O of imaginary octonions and study the relationship of such submanifolds with the geometry of the associative Grassmann manifold $\widetilde{{\rm Gr}}_{ass}$(Im O ) which is the Grassmann manifold of associative subspaces in Im O . Considering the Gauss maps into $\widetilde{{\rm Gr}}_{ass}$(Im O ) associated to Lagrangian submanifolds, we show that those maps are harmonic. Moreover, the Gauss maps associated to homogeneous Lagrangian submanifolds are investigated.
</p>projecteuclid.org/euclid.kmj/1584345693_20200316040132Mon, 16 Mar 2020 04:01 EDTSurfaces in pseudo-Riemannian space forms with zero mean curvature vectorhttps://projecteuclid.org/euclid.kmj/1584345694<strong>Naoya Ando</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 43, Number 1, 193--219.</p><p><strong>Abstract:</strong><br/>
We characterize a space-like surface in a pseudo-Riemannian space form with zero mean curvature vector, in terms of complex quadratic differentials on the surface as sections of a holomorphic line bundle. In addition, combining them, we have a holomorphic quartic differential. If the ambient space is $S^4$, then this differential is just one given in [5]. If the space is $S^4_1$, then the differential coincides with a holomorphic quartic differential in [6] on a Willmore surface in $S^3$ corresponding to the original surface through the conformal Gauss map. We define the conformal Gauss maps of surfaces in $E^3$ and $H^3$, and space-like surfaces in $S^3_1$, $E^3_1$, $H^3_1$ and the cone of future-directed light-like vectors of $E^4_1$, and have results which are analogous to those for the conformal Gauss map of a surface in $S^3$.
</p>projecteuclid.org/euclid.kmj/1584345694_20200316040132Mon, 16 Mar 2020 04:01 EDT