次大体积增长的流形的曲率与拓扑研究  

Research on the curvature and the topology of manifolds with sub-large volwume growth

作　　者：薛琼[1] 陈欢欢[1] 陈爱云[1] 肖小峰[2] XUE Qiong CHEN Huanhuan CHEN Aiyun XIAO Xiaofeng(School of Science, Wuhan University of Technology, Wuhan 430070 School of Mechanical Engineering and Automation, Wuhan Textile University, Wuhan 430073)

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）》2016年第5期652-655,共4页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(61573012);中央高校基本科研业务费专项资金项目(2015IA010)

摘　　要：该文研究了一类具有非负Ricci曲率和α(α∈[0,2])次衰减截曲率下界的完备非紧黎曼流形.利用Toponogov型比较定理和临界点理论,证明了该流形在一定次大体积增长条件下具有有限拓扑型,从而推广了J.Sha、Z.Shen和C.Xia的关于这类流形的一系列结果.In this paper,complete noncompact Riemannian manifolds are studied with nonnegative Ricci curvature and lower bound ofα（α∈ [0,2]）-sectional curvature decay.By Toponogov＇s comparison theorems and critical point theory,the above manifold is demonstrated to have finite topological type with certain sub-large volume growth,which extend these results presented by J.Sha,Z.Shen and C.Xia.

关 键 词：RICCI曲率 次大体积增长 Excess函数 BUSEMANN函数 

分 类 号：C20[社会学]