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Grove-Shiohama 球面直径定理

Posted by haifeng on 2012-03-24 09:19:16 last update 2012-03-24 09:19:16 | Edit | Answers (0)

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.