Pinching theorems of hypersurfaces in a unit sphere

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• 作者：Yun Tao Zhang ;   ; ^{yuntaozhang@xznu.edu.cn}
• 关键词：Hypersurface ; Principle curvature ; Ricci curvature
• 刊名：Differential Geometry and its Applications
• 出版年：2011
• 出版时间：December 2011
• 年：2011
• 卷：29
• 期：6
• 页码：730-736
• 全文大小：161 K

文摘

Let be a complete hypersurface in with constant mean curvature. Assume that has principal curvatures with the same sign everywhere. We prove that if , either or or the fundamental group of is infinite, then S is constant, and is isometric to a Clifford torus with . These rigidity theorems are still valid for compact hypersurface without constancy condition on the mean curvature.