Posted by haifeng on 2012-03-24 09:19:16 last update 2012-03-24 09:19:16 | Answers (0) | 收藏
Grove-Shiohama 的球面直径定理
设 $M^n$ 是一个 $n$ 维完备连通的黎曼流形, 截面曲率 $K_M\geq 1$, 若其直径 $d(M)>\frac{\pi}{2}$, 则 $M^n$ 同胚于球面.
References:
Grove, K. and Shiohama, K.: A generalized sphere theorem Ann. of Math. 106 (1977) 201–211.
