关于Finsler几何中的Hadamard定理

On the Hadamard Theorem in Finsler Geometry

本文利用陈省身最近在Ｆｉｎｓｌｅｒ几何中引进的一个特殊仿射联络，把Ｒｉｅｍａｎｎ几何中关于非正曲率流形的Ｈａｄａｍａｒｄ定理推广到Ｆｉｎｓｌｅｒ几何中．

In this pace,the Hadamard theorem in Riemannfan geometry is generalized to finsler geometry in terms of the speal affine connection intnduced recently by S. S. Chen. The followigng is proved.Theorem:Let M be an n-dimendonal,simply-connected,and complete finsler manifold. If the nag curvatures of M are nonpositive everywhere,then M is diffeomorphic to the euclidean n-space.