非正截曲率的完备Riemann流形在无穷远截曲率趋于零的条件

Condition of Sectional Curvature Tend to Zero at to infinity about Complete Riemannian Manifold with Non-Positive Curvature

中文关键词:  正规测地线  Jaboci场  截曲率

英文关键词:normal geodesic  Jacobi field  sectional curvature.

中文摘要:

      本文给出并证明了定理；设Ｍ为具非正截曲率的完备Ｒｉｅｍａｎｎ流形，Ｔ：［０，＋∞）→Ｍ为Ｍ上的正规测地线，Ｕ是沿Ｔ且初值为零的非平凡正常Ｊａｃｏｂｉ场，若存在ａ＞０，ｔ_０＞０，使得当ｔ≥ｔ_０时．

英文摘要:

      In this paper, we give and prove the following theorem: If M is a complete Riemannian manifold with non-positive curvature, r: [0,+∞ )→M be a normal geodesic on M, U bea non-trivial normal Jacobi field along r and U (0) = 0, and if there is a a> 0,t_０>0 so that(?).