2.
On arachnoid mechanisms formed by concatenation of arc-length parametrized curves - Kamiyama, Yasuhiko
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?. Using this, we determine the homotopy type of the configuration spaces when P is a tetrahedron, cube or octahedron.
3.
On property of complements of an algebraic curve with at least 4 irreducible components in P2 - Adachi, Yukinobu
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 ?M is a curve or empty set, where ?M is the degeneracy locus of the Kobayashi pseudodistance dM on M, coincide with each other.
4.
Totally contact umbilical lightlike hypersurfaces of indefinite Sasakian manifolds - Massamba, Fortuné
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.
5.
On toric hyperkähler manifolds with compact complex submanifolds - Aoto, Yosihiko
A toric hyperkähler manifold is defined as a hyperkähler quotient of the flat quaternionic space HN by a subtorus of the real torus TN. 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 CN by subtori of TN. Finally, we apply these results to determining whether complex structures on our hyperkähler manifold are equivalent.
8.
On the holomorphic invariants for generalized Kähler-Einstein metrics - Sano, Yuji
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 ?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 $\mathbb{CP}^2\sharp \overline{\mathbb{CP}^2}$ admits generalized Kähler-Einstein metrics by the method using...
9.
Division values of multiple sine functions - Koyama, Shin-ya
We refine a formula on values of quadruple sine functions at division points. As applications we prove a formula on a sum of reciprocal trigonometric values, and obtain multiple modularity of a three variable modular function, which concerns a generalization of the Dedekind η function.
10.
The axiom of spheres in semi-Riemannian geometry with lightlike submanifolds - Kumar, Rakesh; Rani, Rachna; Nagaich, R. K.
Let $(\bar{M},\bar{g})$ be a semi-Riemannain manifold and (M, g, S (TM), S (TM⊥)) be its lightlike submanifold. We show that if $\bar{M}$ satisfies the axiom of r-planes & spheres then it is a real space form.
11.
On submanifolds with parallel mean curvature vector - Araújo, Kellcio O.; Tenenblat, Keti
We consider Mn, n ≥ 3, a complete, connected submanifold of a space form $\tilde{M}^{n+p}(\tilde{c})$ , whose non vanishing mean curvature vector H is parallel in the normal bundle. Assuming the second fundamental form h of M satisfies the inequality 2 ≤ n2 |H|2/(n - 1), we show that for $\tilde{c}$ ≥ 0 the codimension reduces to 1. When M is a submanifold of the unit sphere, then Mn is totally umbilic. For the case $\tilde{c}$ < 0, one imposes an additional condition that is trivially satisfied when $\tilde{c}$ ≥ 0. When M is compact and has non-negative Ricci curvature...
12.
Weierstrass product representations of multiple gamma and sine functions - Onodera, Kazuhiro
It is well known that the Weierstrass product representation of the Barnes multiple gamma function Γr(z) can be calculated concretely. However, there has been no study on its explicit formulation. In this paper, its simple formulation is achieved. It is applicable to the Weierstrass product representation of the Vignéras multiple gamma function also. Moreover, the Weierstrass product representation of the Kurokawa multiple sine function Sr(z) is also formulated explicitly.
13.
Pseudo-Jacobi operators and Osserman lightlike hypersurfaces - Atindogbe, Cyriaque; Duggal, Krishan L.
We study pseudo-Jacobi operators associated to algebraic curvature maps on lightlike hypersurfaces M and investigate conditions for an induced Riemann curvature tensor to be an algebraic curvature map on M. Two examples are provided with explicit determination of their pseudo-Jacobi operators. Finally, we introduce the notion of lightlike Osserman hypersurfaces and prove some characterization results.
14.
Types of afforested surfaces - Nakai, Mitsuru; Segawa, Shigeo
We form, what we call, an afforested surface R over a plantation P by foresting with trees Tn (n $\in$ N: the set of positive integers). If all of P and Tn (n $\in$ N) belong to the class ${\mathcal O}_s$ of hyperbolic Riemann surfaces W carrying no singular harmonic functions on W, then we will show that, under a certain diminishing condition on roots of trees Tn (n $\in$ N), the afforested surface R also belongs to ${\mathcal O}_s$ .
16.
Meromorphic functions that share some pairs of small functions - Li, Ping; Yang, Chung-Chun
We discuss possible relations between two meromorphic functions f and g when they share some pairs of small functions. By utilizing the generalized Nevanlinna's second main theorem for small functions obtained recently, we have been able to show that two meromorphic functions f and g must be linked by a quasi-Möbius transformation if they share three pairs of small functions CM* and share another pair of small function IM*. Moreover, we also improves a known result due to T. Czubiak and G. Gundersen on two meromorphic functions sharing five pairs of values and the results on the unicity of meromorphic...
18.
The central value of the triple sine function - Kurokawa, Nobushige
We study the central value of the triple sine function for a general period. We give an explicit integral expression and an inequality. As an application we obtain an expression for ζ(3).
19.
On the distribution of arguments of Gauss sums - Shparlinski, Igor E.
Let Fq be a finite field of q elements of characteristic p. N. M. Katz and Z. Zheng have shown the uniformity of distribution of the arguments arg G (a, χ) of all (q - 1)(q - 2) nontrivial Gauss sums ¶
$G(a, \chi) = \sum_{x \in {\mathbf F}_q} \chi(x) \exp(2 \pi i \mathrm{Tr}(ax)/p),$
¶ where χ is a non-principal multiplicative character of the multiplicative group Fq* and Tr(z) is the trace of z $\in$ Fq into Fp. ¶ Here we obtain a similar result for the set of arguments arg G(a, χ) when a and χ run through arbitrary (but sufficiently...
20.
The Hausdorff dimension of the set of dissipative points for a Cantor-like model set for singly cusped parabolic dynamics - Schmeling, Jörg; Stratmann, Bernd O.
In this paper we introduce and study a certain intricate Cantor-like set $\mathcal{C}$ contained in unit interval. Our main result is to show that the set $\mathcal{C}$ itself, as well as the set of dissipative points within $\mathcal{C}$ , both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.
1.
