We consider arachnoid mechanisms which are formed by concatenation of arc-length parametrized curves in R³ such that the initial point of each curve is fixed to a vertex of a convex polytope P. We prove that the configuration spaces of such arachnoid mechanisms are described in terms of the polar polytope P^Δ. Using this, we determine the homotopy type of the configuration spaces when P is a tetrahedron, cube or octahedron.

For the manifold M := P² - A(l) (l ≥ 4) where A(l) is an algebraic curve with l irreducible components, the notion that M is of log general type, measure hyperbolic and Δ_M is a curve or empty set, where Δ_M is the degeneracy locus of the Kobayashi pseudodistance d_M on M, coincide with each other.

This paper investigates totally contact umbilical lightlike hypersurfaces which are tangent to the structure vector field. Theorems on Killing distributions, geodesibility of lightlike hypersurfaces are obtained. The geometrical configuration of such lightlike hypersurfaces and its screen distributions are established. We prove the non-existence of totally contact umbilical lightlike hypersurfaces and lightlike hypersurfaces with totally contact umbilical screen distributions in indefinite Sasakian space forms under some conditions. Some characterizations of totally contact geodesic lightlike hypersurfaces and screen distributions are also given.

A toric hyperkähler manifold is defined as a hyperkähler quotient of the flat quaternionic space H^N by a subtorus of the real torus T^N. The purposes of this paper are to construct compact complex submanifolds of toric hyperkähler manifolds, and to show that our hyperkähler manifold is a resolution of singularities of an affine algebro-geometric quotient. We also show that these submanifolds are biholomorphic to Delzant spaces, which are Kähler quotients of C^N by subtori of T^N. Finally, we apply these results to determining whether complex structures on our hyperkähler manifold are equivalent.

We consider the torsion points of elliptc curves over certain number fields with good reduction everywhere.

The purpose of this article is to show a uniqueness theorem for meromorphic mappings of C^m into CPⁿ with truncated multiplicities and a small set of identity.

The aim of this paper is to discuss the convergence of a third order Newton-like method for solving nonlinear equations F(x) = 0 in Banach spaces by using recurrence relations. The convergence of the method is established under the assumption that the second Fréchet derivative of F being ω-continuous given by ||F″(x)-F″(y)|| ≤ ω (||x - y||), x, y $\in$ Ω, where ω be a nondecreasing function on R₊ and Ω any open set. This ω-continuity condition is milder than the usual Lipschitz/Hölder continuity condition. To get a priori error bounds, a family of recurrence relations based on two parameters depending on the operator F is also derived. Two numerical examples are worked out to show that the method is successful even in cases where Lipschitz/Hölder continuity condition fails but ω-continuity condition is satisfied. In comparison to the work of Wu and Zhao [15], our method is more general and leads to better results.

In [9], Mabuchi extended the notion of Kähler-Einstein metrics to the case of Fano manifolds with novanishing Futaki invariant. We call them generalized Kähler-Einstein metrics. He defined the holomorphic invariant α_M in terms of the extremal Kähler vector field, which is the obstruction for the existence of generalized Kähler-Einstein metrics. The purpose of this short paper is to show that the above obstruction is actually equivalent to the vanishing of the holomorphic invariant of Futaki's type defined by Futaki [4] (see also [8]). As its corollary, we can show that $\mathbf{CP}^2\sharp \overline{\mathbf{CP}^2}$ admits generalized Kähler-Einstein metrics by the method using multiplier ideal sheaves in [6].