可定向的具非负曲率完备非紧黎曼流形

The Complete Orientable Riemannian Manifold With Nonnegative Curvature

本文研究了具非负曲率完备非紧黎曼流形的一些几何性质，包括闭测地线，体积等．证明了核心的余维数为奇数的可定向具非负曲率完备非紧黎曼流形在其核心的任一法测地线均为射线的条件下可等距分裂为 Ｒ×Ｎ，其中 Ｎ为低一维的流形．

The paper studies some properties of an open Riemannian manifold with nonnegative curvature, including closed geodesics, volume etc. We prove that if the manifold is orientable, if every normal geodesic of its soul is a ray and the codimension of its soul is odd, then the manifold can be isometrically splitting as N × R.