次大体积增长条件下非紧黎曼流形的拓扑结构  

Topological Structure of Complete Open Riemanninn Manifolds with Sub-large Volume Growth

作　　者：陈爱云[1] 薛琼[1] 陈欢欢[1] 肖小峰 CHEN Aiyun;XUE Qiong;CHEN Huanhuan;XIAO Xiaofeng(School of Science,Wuhan University of Technology,Wuhan 430070,Hubei;School of Mechanical Engineering and Automation,Wuhan Textile University,Wuhan 430073,Hubei)

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

出　　处：《四川师范大学学报（自然科学版）》2019年第2期216-220,共5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：研究一类具有非负Ricci曲率和次大体积增长的完备非紧的黎曼流形,利用Toponogov型比较定理和临界点理论,证明在临界半径有正下界以及函数(vol[B(p,r)])/(I_n(r)r^(n-1))是单调递减条件下,流形M微分同胚于R^n,从而丰富了前人关于这类流形的研究结果.In this paper,we study complete noncompact Riemannian manifolds with nonnegative Ricci curvature and sublarge volume growth.By comparison theorems of the Toponogov type and critical point theory,we prove that such a manifold M is diffeomorphic to R^n if its critical radius has positive lower bound and the function vol[B(p,r)]/In(r)r^n-1 is monotone decreasing.We enrich the results proved in previous literature.

关 键 词：RICCI曲率 次大体积增长 Excess函数 Toponogov型比较定理 

分 类 号：O186[理学—数学]