射线截曲率有负下界且大体积增长的开流形  

Open Manifolds with Radial Sectional Curvature Bounded Below and Large Volume Growth

作　　者：陈欢欢[1] 薛琼[1] 陈爱云[1] 李奥 CHEN Huanhuan;XUE Qiong;CHEN Aiyun;LI Ao(School of Science, Wuhan University of Technology, Wuhan 430070, Hube)

机构地区：[1]武汉理工大学理学院,湖北武汉430070

出　　处：《四川师范大学学报（自然科学版）》2018年第1期24-27,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(61573012);中央高校基本科研业务费专项资金(2017IA006)

摘　　要：研究一类具有Ric_M≥-(n-1)c和大体积增长的完备非紧黎曼流形.证明在射线截面曲率有负下界以及流形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R^n.将曲率条件及体积增长条件改进,所得结果是文献(Xia C.London Math Soc,2002,34(2):229-235.)中相关结论的推广.In this paper,we study complete noncompact Riemannian manifolds with Ricci curvature RicM≥-（n-1）c and large volume growth.We prove that such a manifold M is diffeomorphic to R^n if its radial sectional curvature is bounded from below and the volume growth of geodesic balls in M is not too far from that of the balls in R^n.We generalize the result of the literature（XIA C.London Math.Soc.,2002,34（2）：229-235.）by improving curvature and volume growth conditions.

关 键 词：黎曼流形 射线截面曲率 微分同胚 大体积增长 

分 类 号：O175[理学—数学]