具有非负Ricci曲率和次大体积增长的完备流形(英文)  

COMPLETE MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE AND SUB-LARGE VOLUME GROWTH

作　　者：薛琼[1] 肖小峰[2] 

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：《数学杂志》2012年第4期629-636,共8页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10901067);the Fundamental Research Funds for the Central Universities(2011-1a-023)

摘　　要：本文研究了具有非负Ricci曲率和次大体积增长的完备黎曼流形的拓扑结构问题.利用Toponogov型比较定理及临界点理论,获得了流形具有有限拓扑型的结果,推广了H.Zhan和Z.Shen的定理,并且还证明了该流形的基本群是有限生成的.In this paper,we study the topology of complete Riemannian manifolds with nonnegative Ricci curvature and sub-large volume growth.By Toponogov’s comparison theorems and critical point theory,we obtain some results on finite topological type,which improve the theorem proved by H.Zhan and Z.Shen.We also prove that such a manifold has a finitely generated fundamental group.

关 键 词：黎曼流形 RICCI曲率 次大体积增长 有限拓扑型 

分 类 号：O186.12[理学—数学]