Pinching theorems of hypersurfaces in a unit sphere |
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Authors: | Yun Tao Zhang |
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Institution: | Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu 220009, China |
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Abstract: | Let Mn be a complete hypersurface in Sn+1(1) with constant mean curvature. Assume that Mn has n−1 principal curvatures with the same sign everywhere. We prove that if RicM≤C−(H), either S?S+(H) or RicM?0 or the fundamental group of Mn is infinite, then S is constant, S=S+(H) and Mn is isometric to a Clifford torus with . These rigidity theorems are still valid for compact hypersurface without constancy condition on the mean curvature. |
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Keywords: | MSC: 53C42 53B30 |
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