非负Ricci曲率开流形的拓扑(英文)  

The Topology of Open Manifolds with Nonnegative Ricci Curvature

作　　者：杨芳云[1] 徐森林[2] 王作勤[1] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026 [2]华中师范大学数学系,湖北武汉430079

出　　处：《数学研究》2003年第1期1-7,共7页Journal of Mathematical Study

基　　金：National Natural Science Foundation of China (19971081)

摘　　要：我们证明了对于具有非负Rieei曲率,大体积增长且内半径下有界的完备n维Riemann流形,只要存在常数C>0使得 则它微分同胚于欧式空间Rn.我们还证明了在某些pinching条件下具有非负射线曲率的完备n维Riemarm流形微分同胚与Rn,改进了已知的结果.In this paper > we prove that a complete n-dimensional Riemannian manifold with non-negative Ricci curvature, large volume growth and injectivity radius bounded from below is diffeomor- phic to R' provided that for some constant C>0. We also prove that a complete ?dimensional Riemannian manifold with nonnegative radial curvature Kmin, and under some pinched conditions is diffeomorphic to Rn.

关 键 词：Excess函数 大体积增长 射线曲率 体积比较定理 Ricci曲率 开流形 拓扑 RIEMANN流形 欧式空间 

分 类 号：O189[理学—数学]