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

Abstract:

      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(?).