Closed Geodesics and Volume Growth of Open Manifolds with Sectional Curvature Bounded from Below  

作　　者：Yi SHI Guanghan LI Chuanxi WU 

机构地区：[1]Department of Mathematics,Capital Normal University [2]School of Mathematics and Computer Science,and Key Laboratory of Applied Mathematics of Hubei Province,Hubei University [3]Institute of Mathematics,Hubei University

出　　处：《Chinese Annals of Mathematics,Series B》2014年第1期93-100,共8页数学年刊（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10971055,11171096);the Research Fund for the Doctoral Program of Higher Education of China(No.20104208110002);the Funds for Disciplines Leaders of Wuhan(No.Z201051730002)

摘　　要：In this paper, the relationship between the existence of closed geodesics and the volume growth of complete noncompact Riemannian manifolds is studied. First the authors prove a diffeomorphic result of such an n-m2nifold with nonnegative sectional curvature, which improves Marenich-Toponogov＇s theorem. As an application, a rigidity theorem is obtained for nonnegatively curved open manifold which contains a clesed geodesic. Next the authors prove a theorem about the nonexistence of closed geodesics for Riemannian manifolds with sectional curvature bounded from below by a negative constant.

关 键 词：Closed geodesic Sectional curvature Volume growth 

分 类 号：O186.11[理学—数学]