关于3维负曲率流形的拓扑型(英文)  

On the Topological Type of 3-dimensional Negatively Curved Manifolds

作　　者：周青[1] 

机构地区：[1]华东师范大学数学系

出　　处：《数学进展》1993年第3期270-281,共12页Advances in Mathematics（China）

基　　金：Supported in part by NSFC Grant 19141002 and a FEYUT of SEDC of China

摘　　要：本文的主要定理是:对每一个正数V,存在一个D>0,如果一个3维黎曼流形M的体积小于V,截面曲率在-1和0之间,而且直径大于D,那么M允许一个双曲结构。The main theorem in this paper is the following: for any positive number V, there is a D>0.such that any 3-dimensional Riemannian manifold M with volume not larger than V, sectional curvature between -1 and 0, and diameter larger than D admits a hyperbolic structure.

关 键 词：负曲率流形 双曲结构 拓扑型 流形 

分 类 号：O189[理学—数学]