On the Pesin set of expansive geodesic flows in manifolds with no conjugate points

In this paper, we show that the Pesin set of an expansive geodesic flow in compact manifold with no conjugate points and bounded asymptote coincides a.e with an open and dense set of the unit tangent bundle. We also show that the set of hyperbolic periodic orbits is dense in the unit tangent bundle.     

关于切丛和单位切球丛的度量的一个注记

本文在黎曼流形$(M,g)$的切丛$TM$ 上研究与参考文献[10]中平行的一类度量$G$以及相容的近复结构$J$.证明了切丛$TM$关于这些度量和相应的近复结构是局部共形近K\"{a}hler流形,并且把这些结构限制在单位切球丛上得到了切触度量结构的新例子.     

On the tangent spaces of Chow groups of certain projective hypersurfaces

In this paper, the Chow groups of projective hypersurfaces are studied. We will prove that if the degree of the hypersurface is sufficiently high, its Chow group is ``small' in the sense that its formal tangent space vanishes. Then, we will give an example in which the formal tangent space is infinite dimensional.

     

Maximally movable spaces of Finsler type and their generalization

In this paper, we consider some generalization of maximally movable spaces of Finsler type. Among them, there are locally conic spaces (Riemannian metrics of their tangent spaces are realized on circular cones) and generalized Lagrange spaces with Tamm metrics (their tangent Riemannian spaces admit all rotations). On the tangent bundle of a Riemannian manifold, we study a special class of almost product metrics, generated Tamm metric. This class contains Sasaki metric and Cheeger–Gromol metric. We determine the position of this class in the Naveira classification of Riemannian almost product metrics.     

Compactness theorems and the Calabi flow on Kähler surfaces with stable tangent bundle

Abstract. In this paper, we prove some compactness theorems and collapse phenomenon on compact K?hler surfaces with stable tangent bundle. We then apply the results to the Calabi flow. More precisely, we prove, under suitable curvature conditions, the longtime existence and asymptotic convergence for solutions of the Calabi flow on compact K?hler surfaces admitting no nonzero holomorphic tangent vector fields and with stable tangent bundle. We also give some examples where the Calabi flow blows up. Received January 7, 1999 / Revised February 2, 2000 / Published online July 20, 2000     

On the finiteness of differential invariants

In this paper we show how Weil's theory of near points yields a new light on the classical approaches to the study of the differential invariants of a sheaf of tangent vector fields. We give conditions for the existence of invariant derivations for a sheaf of tangent vector fields, which allows to apply Lie's algorithm to obtain new differential invariants as quotients of Jacobian determinants of known ones. We give sufficient conditions for the asymptotic stability of the symbol of a sheaf of tangent vector fields and prove our main result, a finiteness theorem for the differential invariants of a sheaf of Lie algebras which simplifies and improves on the treatment given in J. Differential Geom. 10 (1975) 249-416.     

Homogeneous numerical semigroups

We introduce the concept of homogeneous numerical semigroups and show that all homogeneous numerical semigroups with Cohen–Macaulay tangent cones are of homogeneous type. In embedding dimension three, we classify all numerical semigroups of homogeneous type into numerical semigroups with complete intersection tangent cones and the homogeneous ones which are not symmetric with Cohen–Macaulay tangent cones. We also study the behavior of the homogeneous property by gluing and shiftings to construct large families of homogeneous numerical semigroups with Cohen–Macaulay tangent cones. In particular we show that these properties fulfill asymptotically in the shifting classes. Several explicit examples are provided along the paper to illustrate the property.     

Earthquake曲线切向量上的范数

本文研究了定义在earthquake曲线切向量上的范数，首先证明了一条earthquake曲线ht上初始切向量的范数等价于earthquake测度σ的Thurston范数．其次证明了当t→∞时，ht的切向量Vt的范数增长渐近等于O(||→||The^Ct||σ||Th)，其中C是正的万有常数，||σ||Th是σ的Thurston范数，而O所代表的常数是渐近万有的，也即当t||σ||Th充分大时它是万有的．此外，附带证明了定义在Zygmund有界函数上的两种交比范数是等价的．     

A note on the discrete approximation of discontinuous curves and surfaces

This is a note on the paper [A. Kouibia, A.J. López-Linares, M. Pasadas, Approximation of discontinuous curves and surfaces with tangent conditions, J. Comput. Appl. Math. 193 (2006) 51–64]. We consider the constructing problem of a discontinuous parametric curve or surface from a finite set of points and tangent conditions. We develop a method based on the theory of discrete smoothing variational splines conveniently adapted to introduce the tangent conditions and the discontinuity set. We give a convergence result and we analyze some numerical and graphical examples in order to illustrate the effectiveness of the presented method.     

On doubly warped product Finsler manifolds

In this paper, we introduce horizontal and vertical warped product Finsler manifolds. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemannian curvatures of doubly warped product Finsler manifold and its components, and consider the cases that this manifold is flat or has scalar flag curvature. We define the doubly warped Sasaki-Matsumoto metric for warped product manifolds and find a condition under which the horizontal and vertical tangent bundles are totally geodesic. We obtain some conditions under which a foliated manifold reduces to a Reinhart manifold. Finally, we study an almost complex structure on the tangent bundle of a doubly warped product Finsler manifold.     

集值向量优化的二阶最优性必要条件

在赋范空间中给出了集值映射的二阶切集的概念,利用二阶切集,定义了集值映射的二阶切导数。然后,获得了集值向量优化问题弱极小元的两个二阶最优性必要条件。     

度量方程应用于Krause定理的推广

本文用距离几何的方法证明了主要定理,对曲率为Ｋ的ｎ维常曲率空间,其内任意ｎ＋１个ｎ－１维球Ｓｉ（ｉ＝１,２,…,ｎ＋１）,它们中的任一个都与其它球不变,则与Ｓｉ交角为βｉ（ｉ＝１,２,…,ｎ＋１）的ｎ－１维一般有２＾ｎ＋１个,当ｎ为偶数时,它们的测地线曲率之交错和为零;当ｎ为奇数时,此结论不成立,该定理包括非欧情形,而当ｎ＝２,βｉ＝１（ｉ＝１,２,…,ｎ＋１）时,就是ｉｉｌｋｅｒＪＢ在「１」中所     

Differential Structure,Tangent Structure,and SDG

In 1984, J. Rosický gave an abstract presentation of the structure associated to tangent bundle functors in differential and algebraic geometry. By slightly generalizing this notion, we show that tangent structure is also fundamentally related to the more recently introduced Cartesian differential categories. In particular, tangent structure of a trivial bundle is precisely the same as Cartesian differential structure. We also provide a general result which shows how tangent structure arises from the manifold completion (in the sense of M. Grandis) of a differential restriction category. This construction includes all standard atlas-based constructions from differential geometry. Furthermore, we tighten the relationship, which Rosický had noted, between representable tangent structure and synthetic differential geometry, showing how such settings can be developed from a system of infinitesimal objects. We also show how infinitesimal objects give rise to dual tangent structure. Taken together, these results show that tangent structures appropriately span a very wide range of definitions, from the syntactic and structural differentials arising in computer science and combinatorics, through the concrete manifolds of algebraic and differential geometry, and finally to the abstract definitions of synthetic differential geometry.     

一些流形的复化切丛的平凡性

本文研究一个流形M的复化切丛TcM的平凡性问题。我们证明当M是n维球面S^n或者满足某些条件的2,3或4维流形时,TcM是平凡丛．     

Effective Circle Count for Apollonian Packings and Closed Horospheres

The main result of this paper is an effective count for Apollonian circle packings that are either bounded or contain two parallel lines. We obtain this by proving an effective equidistribution of closed horospheres in the unit tangent bundle of a geometrically finite hyperbolic 3-manifold, whose fundamental group has critical exponent bigger than 1. We also discuss applications to affine sieves. Analogous results for surfaces are treated as well.     

一类平面三次拟齐次向量场的全局拓扑结构

利用中心投影变换的思想证明一类平面三次拟齐次向量场的几何性质依赖于它的切向量场和诱导向量场.讨论了该系统的拓扑结构,并进行了分类;证明了该系统具有25类不同类的拓扑结构相图.     

Dual-holomorphic Functions and Problems of Lifts

The main purpose of this paper is to study the differential geometrical objects on tangent bundle corresponding to dual-holomorphic objects of dual-holomorphic manifold.As a result of this approach, the authors find a new class of lifts(deformed complete lifts)in the tangent bundle.     

The blow-up curve of solutions of mixed problems for semilinear wave equations with exponential nonlinearities in one space dimension, II

In this paper, we consider mixed problems with a timelike boundary derivative (or a Dirichlet) condition for semilinear wave equations with exponential nonlinearities in a quarter plane. The case when the boundary vector field is tangent to the characteristic which leaves the domain in the future is also considered. We show that solutions either are global or blow up on a C¹ curve which is spacelike except at the point where it meets the boundary; at that point, it is tangent to the characteristic which leaves the domain in the future.     

Automorphisms and a reduction theorem in a Sasakian space form E2m+1(−3)

Summary We construct definitely the automorphism group of a Sasakian space form ¯M=E ^2m+1 (–3) and study the existence of a totally geodesic invariant submanifold of ¯M tangent to a given invariant subspace in the tangent space of ¯M. We also study the Frenet curves in ¯M under a totally contact geodesic immersion of a contact CR-submanifold into ¯M. The purpose of this paper is to prove a reduction theorem of the codimension for a totally contact geodesic, contact CR-submanifold of ¯M.     

一类带有给定切线多边形的样条曲线

利用带有形状参数的基函数,构造与给定切线多边形相切的样条曲线,所构造的曲线是C2和C3连续的,且对切线多边形是保形的.曲线上的所有控制点可由多边形顶点直接计算产生,曲线具有局部修改性.最后,以实例说明算法是有效的.