Characterizations of a Clifford hypersurface in a unit sphere via Simons’ integral inequalities

详细信息    查看全文

• 作者：Sung-Hong Min ; Keomkyo Seo
• 关键词：Clifford hypersurface ; Simons’ integral inequality ; Ricci curvature ; Higher ; order mean curvature
• 刊名：Monatshefte f¨¹r Mathematik
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：181
• 期：2
• 页码：437-450
• 全文大小：428 KB
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：181

文摘

Let M be an \(n(\ge \)3)-dimensional closed hypersurface in a unit sphere with constant m-th order mean curvature and with two distinct principal curvatures. We obtain a sharp curvature integral for M in terms of Ricci curvature, which gives a characterization of a Clifford hypersurface. Moreover we give a generalization of Simons’ integral inequality for closed hypersurface with vanishing m-th order mean curvature by making use of the Laplacian of the function of principal curvatures.