核心的余维数为1的具非负曲率完备非紧黎曼流形

The Complete Open Nonnegatively Curved Riemannian Manifolds with Souls of Codimension one

利用G .Perelman证明“核心猜想”的思想证明了对n维完备非紧具非负曲率的黎曼流形 ,若其核心之维数是n - 1,则该流形可等距分裂为S×R .其中S为该流形的核心 .

Let M be a complete open Riemannian Manifold with nonnegative curvature, S be its soul. Suppose that dim S =dim M-1, then M=S×R, where '=' represents isometry. Perelman′s idea of solving the soul conjecture plays a key role in our proof.