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

作　　者：夏大峰[1] 徐森林[2] 祁锋[2] 

机构地区：[1]阜阳师范学院数学系,安徽236032 [2]中国科学技术大学数学系,合肥230026

出　　处：《Journal of Mathematical Research and Exposition》1999年第4期747-752,共6页数学研究与评论（英文版）

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，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.

关 键 词：正规测地线 截曲率 黎曼流形 无穷远截曲率 

分 类 号：O186.12[理学—数学]