科研之友
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摘要
We prove a vanishing theorem for the fundamental group of a compact submanifold in a space form, and then present a refined version of Ejiri's rigidity theorem for minimal submanifolds in a sphere. Inspired by the refined Ejiri theorem, we verify a new differentiable sphere theorem for compact submanifolds in space forms. We also show that our differentiable sphere theorem is sharp. We emphasize that our method of Ricci flow in the proof of the sphere theorem seems useful in the study of curvature and topology. Also, we obtain a differentiable pinching theorem for compact submanifolds in a Riemannian manifold.
- 出版日期2011-12
- 单位浙江大学
