黎曼流形上度量的Ricci流的一个定理

A THEOREM OF RICCI FLOW OF METRIC ON RIEMANNIAN MANIFOLD

利用Huisken的热流方法 ,推广了Hamilton的 3维Ricci流的著名结果 .证明了一个球面定理 :如果黎曼曲率张量的模长和它的数量曲率分量U的模长的比接近于 1,则M容许一个正的常曲率的度量 .

A sphere theorem is proved. If the ratio of the norms of Riemannian curvature tensor to its scalar curvature part of M is close to one, then M admits a metric with constant positive curvature. By using Huiskens method, it is generalized to a well known result due to Hamilton.