具有渐近非负Ricci曲率完备非紧的黎曼流形  

Complete noncompact Riemannian manifold with asymptotically nonnegative Ricci curvature

作　　者：陈爱云[1] 薛琼[1] 陈欢欢[1] 肖小峰 CHEN Ai-yun;XUE Qiong;CHEN Huan-huan;XIAO Xiao-feng(School of Science, Wuhan University of Technology, Wuhan 430070, Hubei, China;School of Mechanical Engineering and Automation, Wuhan Textile University, Wuhan 430073, Hubei, China)

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：《山东大学学报（理学版）》2018年第4期1-6,共6页Journal of Shandong University(Natural Science)

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

摘　　要：研究了一类具有渐近非负Ricci曲率完备非紧的n维黎曼流形,利用推广的Excess函数和Busemann函数,证明了具有渐近非负Ricci曲率完备非紧的n维黎曼流形在k_p(r)≥-C/(1+r)α和大体积增长的条件下具有有限拓扑型,从而推广了已有的一系列结果。We study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature.By using extensions of Excess function and Busemann function,it is proved that they have finite topological type under sectional curvature bounded from nonnegative belowk_p（r） ≥-C/（1＋ r）α and large volume growth,which extend a series known results.

关 键 词：渐近非负Ricci曲率 Excess函数 BUSEMANN函数 大体积增长 有限拓扑型 

分 类 号：O186[理学—数学]