证明秩为1的紧致对称空间的截面曲率有下界1, 并且直径为 $\pi/2$.
由于此结果, Grove-Shiohama 的球面直径定理对于截面曲率以1为下界的完备流形来说是最优的.
References:
Shiohama, K. and Xu, H., The topological sphere theorem for complete submanifolds, Compositio Math. 107 (1997), 221 – 232.
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