Ricci曲率,共轭半径和大体积增长  

Ricci curvature,conjugate radius and large volume growth

作　　者：薛琼[1] 肖小峰[2] 陈欢欢[1] 

机构地区：[1]武汉理工大学理学院,武汉430070 [2]武汉纺织大学机械工程与自动化学院,武汉430073

出　　处：《华中师范大学学报（自然科学版）》2015年第3期331-333,共3页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11201357;11201358);中央高校基本科研业务费专项资金项目(2015IA010)

摘　　要：研究了一类具有非负Ricci曲率和大体积增长的完备非紧黎曼流形.证明了在共轭半径有正下界以及流形M上测地球与欧氏空间上单位球的体积增长相差不大的条件下,流形M微分同胚于Rn.该文将体积增长条件改进,推广了M.Do.Carmo和C.Xia的结果.In this paper, complete noncompact Riemannian manifolds with nonnegative Ricci curvature and large volume growth were studied. We prove that such a manifold M is diffeomorphic to a Euclidean n-space R＂ if its conjugate radius has positive lower bound and the volume growth of geodesic balls in Mis not too far from that of the balls in R^n. We extended the result of M. Do. Carmo and C. Xia by improving volume growth conditions.

关 键 词：RICCI曲率 大体积增长 共轭半径 Excess函数 

分 类 号：O186[理学—数学]