Recursos de colección
Bejancu, Aurel
Let F^{m} = (M, F) be a Finsler manifold and G be the Sasaki-Finsler metric on TM°. We show that the curvature tensor field of the Levi-Civita connection on (TM°, G) is completely determined by the curvature tensor field of Vrănceanu connection and some adapted tensor fields on TM°. Then we prove that (TM°, G) is locally symmetric if and only if F^{m} is locally Euclidean. Also, we show that the flag curvature of the Finsler manifold F^{m} is determined by some sectional curvatures of the Riemannian manifold (TM°, G). Finally, for any c ≠ 0 we introduce the c-indicatrix...
Maeda, Masaya
Harui, Takeshi; Komeda, Jiryo; Ohbuchi, Akira
We completely classify the pairs of two smooth plane curves with double coverings between them. More precisely, we show that there exist no double coverings between two smooth plane curves except for several special cases.
Fukuma, Yoshiaki
Let X be a projective variety of dimension n defined over the field of complex numbers and let L_{1}, ..., L_{n-i} be ample line bundles on X, where i is an integer with 0 ≤ i ≤ n. In this paper, first, we define some invariants called the ith sectional H-arithmetic genus, the ith sectional geometric genus and the ith sectional arithmetic genus of (X,L_{1}, ..., L_{n-i}). These are considered to be a generalization of invariants which have been defined in our previous papers. Moreover we investigate some basic properties of these, which are used in the second part and...
Plénat, Camille; Popescu-Pampu, Patrick
Let (X,0) be a germ of complex analytic normal variety, non-singular outside 0. An essential divisor over (X,0) is a divisorial valuation of the field of meromorphic functions on (X,0), whose center on any resolution of the germ is an irreducible component of the exceptional locus. The Nash map associates to each irreducible component of the space of arcs through 0 on X the unique essential divisor intersected by the strict transform of the generic arc in the component. Nash proved its injectivity and asked if it was bijective. We prove that this is the case if there exists a...
Ganchev, Georgi; Milousheva, Velichka
For a two-dimensional surface M^{2} in the four-dimensional Euclidean space E^{4} we introduce an invariant linear map of Weingarten type in the tangent space of the surface, which generates two invariants k and κ. ¶ The condition k = κ = 0 characterizes the surfaces consisting of flat points. The minimal surfaces are characterized by the equality κ^{2} - k = 0. The class of the surfaces with flat normal connection is characterized by the condition κ = 0. For the surfaces of general type we obtain a geometrically determined orthonormal frame field at each point and derive Frenet-type derivative...
Oka, Mutsuo
Polar weighted homogeneous polynomials are special polynomials of real variables x_{i}, y_{i}, i = 1, ..., n with z_{i} = x_{i} + $\sqrt{-1}y_i$ which enjoy a "polar action". In many aspects, their behavior looks like that of complex weighted homogeneous polynomials. We study basic properties of hypersurfaces which are defined by polar weighted homogeneous polynomials.
Wang, Jian-Ping; Huang, Ling-Di
This paper studies the uniqueness of meromorphic functions that share three values CM and obtain some results that are improvements and generalizations of that of H. Ueda, G. Brosch, etc.
Wu, Zhao-jun; Sun, Dao-chun
In this paper, by using Ahlfors' theory of covering surface, the existence of T direction of meromorphic function concerning multiple values is obtained. Results are obtained extending the previous results due to Guo, Zheng, Ng in Bull. Austral. Math. Soc., 69 (2004), 277-287. Moreover, we give an affirmative answer to the question by Wang and Gao in Bull. Austral. Math. Soc., 75 (2007), 459-468.
Noda, Takumi
We give an explicit formula for the zeros of the Rankin type zeta-function by using the projection of the C^{∞}-automorphic forms introduced by Sturm (1981). Our theorem gives a correlation of the zeros of the L-functions and the Hecke eigenvalues.
Seo, Keomkyo
Let M be an n-dimensional complete minimal submanifold in R^{n+p}. Lei Ni proved that if M has sufficiently small total scalar curvature, then M has only one end. We improve the upper bound of total scalar curvature. We also prove that if M has the same upper bound of total scalar curvature, there is no nontrivial L^{2} harmonic 1-form on M.
Kin, Eiko; Takasawa, Mitsuhiko
The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this paper, we study the dilatation of a special family of pseudo-Anosov braids. We prove an inductive formula to compute their dilatation, a monotonicity and an asymptotic behavior of the dilatation for this family of braids. We also give an example of a family of pseudo-Anosov braids with arbitrarily small dilatation such that the mapping torus obtained from such braid has 2 cusps and has an arbitrarily large volume.
Ōshima, Hideaki
The author studies the quotient group $\mathscr{E}$ (SO(4))/ $\mathscr{E}$ _{#}(SO(4)), where $\mathscr{E}$ (SO(4)) is the group of homotopy classes of self homotopy equivalences of the rotation group SO(4) and $\mathscr{E}$ _{#}(SO(4)) is the subgroup of it consisting of elements that induce the identity on homotopy groups.
Bonfert-Taylor, Petra; Falk, Kurt; Taylor, Edward C.
Let G be a discrete quasiconformal group preserving B^{3} whose limit set Λ(G) is purely conical and all of ∂B^{3}. Let Ĝ be a non-elementary normal subgroup of G: we show that there exists a set $\mathcal{A}$ of full measure in Λ(G) so that $\mathcal{A}$ , regarded as a subset of Λ (Ĝ), has "fat horospherical" dynamics relative to Ĝ. As an application we will bound from below the exponent of convergence of Ĝ in terms of the Hausdorff dimension of $\mathcal{A}$ .
Yang, Mingbo; Li, Ping
By utilizing Nevanlinna's value distribution theory, we find the meromorphic solutions of the functional equations of the type P(f)P(g) = 1, where P is a polynomial with three distinct zeros at least.
Sahin, Bayram
It is shown that any horizontally conformal submersion of a CR-submanifold M of a Kaehler manifold $\bar{M}$ onto a Kaehler manifold N is a Riemannian submersion. Moreover, if M is mixed geodesic, then it is proved that such submersion is a harmonic map.
Kimura, Makoto
Konno, Kazuhiro
Fibred rational surfaces with a certain extremal property are classified.
Sankaran, G. K.
Chen, Ten-Ging; Chen, Keng-Yan; Tsai, Yen-Lung
We generalize Nevanlinna's five-value theorem to the cases that two meromorphic functions partially sharing either five or more values, or five or more small functions. In each case, we formulate a way to measure how far these two meromorphic functions are from sharing either values or small functions, and use this measurement to get some uniqueness results.