径向曲率的一个拓扑球面定理

A TOPOLOGICAL SPHERE THEOREM ABOUT RADIAL CURVATURE

设Ｍ是ｎ维连通完备黎曼流形，ｐ∈Ｍ，其径向曲率Ｋｍｉｎｐ≥１，若ｄ（ｐ）＝ｄ（Ｍ）＞π／２，则Ｍ与Ｓｎ同胚，这里ｄ（ｐ）：＝ｓｕｐｘ∈Ｍｄ（ｐ，ｘ），ｄ（·，·）为Ｍ上的距离函数。

Let M be an ndimension connect complete Riemannian manifold,p∈M,its minimal radial curvature Kminp≥1 ,if d(p)=d(M)>π/2,then M is homeomorphic to Sn,where d(p)=supq∈Md(p,q),d(·,·) is the distance function on M ,d(M) is the diameter of M.