局部对称流形上的数量曲率  

THE CURVATURE OF A LOCALLY SYMMETRIC MANIFOLD

作　　者：詹华税[1] 

机构地区：[1]厦门水产学院

出　　处：《数学杂志》1997年第2期257-260,共4页Journal of Mathematics

基　　金：福建省自然科学基金;厦门水产学院青年专项科研基金

摘　　要：本文讨论了无共轭点测地线上的Ｊａｃｏｂｉ声，证明了具非负数量曲率的局部对称的无共轭点流形及具非负数量曲率的具极点的局部对称的流形之数量曲率只能是零．部分解决了Ｅ．In the paper,we discuss the Jacobi field along a geodesic without conjugate points,prove that if M is a locally symmetric manifold without conjugate points and its scalar curvature is nonnegative,then the scalar curvature must be zero and thus we can partly solve E.Hopf conjecture.We also get the conclusion about a manifold with a pole and with nonnegative scalar curvature.

关 键 词：共轭点 测地线 数量曲率 Hopf猜想 局部对称流形 

分 类 号：O186.12[理学—数学]