局部对称空间上的闭测地线  

The Closed Geodesics in a Compact Local Symmetric Space

作　　者：詹华税[1] 

机构地区：[1]厦门大学数学系,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2003年第2期150-152,共3页Journal of Xiamen University：Natural Science

摘　　要：讨论了曲率定号的完备黎曼流形上的平行向量场与Jacobi场之间的关系;证明了紧致的偶数维具非负曲率的非单连通局部对称空间上存在无穷多条长度一样的闭测地线.The paper discusses the relations between parallel vector fields and Jacobi fields in a complete Riemannian manifold, and proves that there exists infinite closed geodesics in a local symmetric space which is orientable, compact, nonsimply connected and with nonnegative sectional curvature.

关 键 词：局部对称空间上 闭测地线 完备黎曼流形 平行向量场 JACOBI场 非负曲率 

分 类 号：O186.12[理学—数学]