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 withNon-Positive Curvature

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，ｔ０＞０，使得当ｔ≥ｔ０时，有Ｕ（ｔ）≤ｔ，且ｌｉｍ Ｋ（Ｕ）（ｔ）存在，则ｌｉｍ Ｋ（Ｕ）（ｔ）＝０．

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,to>0 so thatU (t) with to, and limK (U)=(t) =0 existence, then limK(rU)(t)=0.