Rigidity and sphere theorem for manifolds with positive Ricci curvature |
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Authors: | Changyu Xia |
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Affiliation: | (1) Department of Mathematics, University of Science and Technology of China, 230026 Hefei, Anhui, P. R. China;(2) Mathematical Institute, Tohoku University, 980 Sendai, Japan |
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Abstract: | LetM be a complete Riemannian manifold with Ricci curvature having a positive lower bound. In this paper, we prove some rigidity
theorems forM by the existence of a nice minimal hypersurface and a sphere theorem aboutM. We also generalize a Myers theorem stating that there is no closed immersed minimal submanifolds in an open hemisphere to
the case that the ambient space is a complete Riemannian manifold withk-th Ricci curvature having a positive lower bound.
Supported by the JSPS postdoctoral fellowship and NSF of China |
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Keywords: | 53C20 53C42 |
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