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 共查询到19条相似文献,搜索用时 78 毫秒
1.
可定向的具非负曲率完备非紧黎曼流形   总被引:5,自引:0,他引:5  
詹华税 《数学进展》2001,30(1):70-74
本文研究了具非负曲率完备非紧黎曼流形的一些几何性质,包括闭测地线,体积等.证明了核心的余维数为奇数的可定向具非负曲率完备非紧黎曼流形在其核心的任一法测地线均为射线的条件下可等距分裂为R×N,其中N为低一维的流形.  相似文献   

2.
具非负Ricci曲率和严格(1+δ)阶体积增长的三维流形   总被引:1,自引:1,他引:0  
本文研究了三维完备非紧具非负Ricci曲率的黎曼流形的几何拓扑性质.通过对流形本身与流形的万有覆盖空间体积增长阶的比较,证明了对具非负Ricci曲率和严格(1+δ)阶体积增长的三维完备非紧的黎曼流形是可缩的.  相似文献   

3.
完备Riemann流形之共轭点   总被引:14,自引:0,他引:14  
詹华税 《数学学报》1994,37(3):414-419
本文证明了具非负曲率完备Riemann测地线为无共轭点测地线的充要条件;并由此证明了若该流形上的截面含有一无共轭点测地线的切向量,则其对应的截曲率为零.  相似文献   

4.
完备非紧具非负曲率流形之拓扑结构   总被引:2,自引:1,他引:1  
本文给出完备非紧具非负曲率的Riemann流形具有限拓扑型的一个简单证明.  相似文献   

5.
利用沿测地线的N-Jacobi场和指标形式,得到了具非负曲率完备Riemann流形中的测地子流形为无焦点的充要条件。  相似文献   

6.
杨义虎 《数学学报》2003,46(2):303-308
本文研究了无穷远处具非负截曲率的完备非紧流形的几何和解析性质,并将 它应用于调和映照.  相似文献   

7.
本文给出完备非紧具非负曲率的Riemann流形具有限拓扑型的一个简单证明  相似文献   

8.
设Ω为R~n中有界单连通开集.其边界Ω是无限可微的封闭超曲面.在[7]中建立了同Ω的平均曲率有关的积分等式.本文给出Ω具有非负平均曲率的充要条件.给出Ω具有非负Gauss曲率的充要条件.引用[8]的一个结果,给出Ω具有各阶非负平均曲率的充要条件.  相似文献   

9.
局部对称流形上的数量曲率   总被引:3,自引:0,他引:3  
詹华税 《数学杂志》1997,17(2):257-260
本文讨论了无共轭点测地线上的Jacobi声,证明了具非负数量曲率的局部对称的无共轭点流形及具非负数量曲率的具极点的局部对称的流形之数量曲率只能是零。部分解决了E.Hopf猜想。  相似文献   

10.
设M为de Sitter空间S1^n 1(1)中的完备(非紧)类空超曲面,具有常平均曲率和非负截曲率,在适当条件下,我们证明了它与欧式空间或者双曲柱面等距。  相似文献   

11.
The concept of generalized geodesic curvature is introduced along with the invariant mean geodesic curvature vector for a two-dimensional Pfaffian manifold inE 4, and the indicatrix of generalized geodesic curvature of integral curves of this manifold is constructed.It is proved that the ratio of the fourth quadratic form of the manifold to its first fundamental form is equal to the square of the modulus of the generalized geodesic curvature vector, and an analog of a theorem of Euler is deduced.Translated from Ukrainskií Geometricheskií Sbornik, Issue 28, 1985, pp. 22–26.  相似文献   

12.
In this paper, we study the impact of geodesic vector fields (vector fields whose trajectories are geodesics) on the geometry of a Riemannian manifold. Since, Killing vector fields of constant lengths on a Riemannian manifold are geodesic vector fields, leads to the question of finding sufficient conditions for a geodesic vector field to be Killing. In this paper, we show that a lower bound on the Ricci curvature of the Riemannian manifold in the direction of geodesic vector field gives a sufficient condition for the geodesic vector field to be Killing. Also, we use a geodesic vector field on a 3-dimensional complete simply connected Riemannian manifold to find sufficient conditions to be isometric to a 3-sphere. We find a characterization of an Einstein manifold using a Killing vector field. Finally, it has been observed that a major source of geodesic vector fields is provided by solutions of Eikonal equations on a Riemannian manifold and we obtain a characterization of the Euclidean space using an Eikonal equation.  相似文献   

13.
Let M be a geometrically finite pinched negatively curved Riemannian manifold with at least one cusp. Inspired by the theory of Diophantine approximation of a real (or complex) number by rational ones, we develop a theory of approximation of geodesic lines starting from a given cusp by ones returning to it. We define a new invariant for M, theHurwitz constant of M. It measures how well all geodesic lines starting from the cusp are approximated by ones returning to it. In the case of constant curvature, we express the Hurwitz constant in terms of lengths of closed geodesics and their depths outside the cusp neighborhood. Using the cut locus of the cusp, we define an explicit approximation sequence for a geodesic line starting from the cusp and explore its properties. We prove that the modular once-punctured hyperbolic torus has the minimum Hurwitz constant in its moduli space. Received: 24 October 2000; in final form: 10 November 2001 / Published online: 17 June 2002  相似文献   

14.
In this paper, we introduce a new class of sets and a new class of functions called geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold. The concept of E-quasiconvex functions on R n is extended to geodesic E-quasiconvex functions on Riemannian manifold and some of its properties are investigated. Afterwards, we generalize the notion of epigraph called E-epigraph and discuss a characterization of geodesic E-convex functions in terms of its E-epigraph. Some properties of geodesic E-convex sets are also studied.  相似文献   

15.
It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

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16.
We consider the existence of simple closed geodesics or “geodesic knots” in finite volume orientable hyperbolic 3-manifolds. Every such manifold contains at least one geodesic knot by results of Adams, Hass and Scott in (Adams et al. Bull. London Math. Soc. 31: 81–86, 1999). In (Kuhlmann Algebr. Geom. Topol. 6: 2151–2162, 2006) we showed that every cusped orientable hyperbolic 3-manifold in fact contains infinitely many geodesic knots. In this paper we consider the closed manifold case, and show that if a closed orientable hyperbolic 3-manifold satisfies certain geometric and arithmetic conditions, then it contains infinitely many geodesic knots. The conditions on the manifold can be checked computationally, and have been verified for many manifolds in the Hodgson-Weeks census of closed hyperbolic 3-manifolds. Our proof is constructive, and the infinite family of geodesic knots spiral around a short simple closed geodesic in the manifold.   相似文献   

17.
In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous pseudo‐Riemannian manifold admits a homogeneous geodesic through arbitrary point. In the present paper this affine method is refined and adapted to the pseudo‐Riemannian case. Using this method and elementary topology it is proved that any homogeneous Lorentzian manifold of even dimension admits a light‐like homogeneous geodesic. The method is illustrated in detail with an example of the Lie group of dimension 3 with an invariant metric, which does not admit any light‐like homogeneous geodesic.  相似文献   

18.
In this article, we consider the entropy-expansiveness of geodesic flows on closed Riemannian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.  相似文献   

19.
Generalizing results of Cohn-Vossen and Gromoll, Meyer for Riemannian manifolds and Hawking and Penrose for Lorentzian manifolds, we use Morse index theory techniques to show that if the integral of the Ricci curvature of the tangent vector field of a complete geodesic in a Riemannian manifold or of a complete nonspacelike geodesic in a Lorentzian manifold is positive, then the geodesic contains a pair of conjugate points. Applications are given to geodesic incompleteness theorems for Lorentzian manifolds, the end structure of complete noncompact Riemannian manifolds, and the geodesic flow of compact Riemannian manifolds.Partially supported by NSF grant MCS77-18723(02).  相似文献   

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