Generalized Ejiri's Rigidity Theorem for Submanifolds in Pinched Manifolds

被引：1
|
作者：
Xu, Hongwei [1 ]
Lei, Li [1 ]
Gu, Juanru [1 ,2 ]
机构：
[1] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Peoples R China
[2] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310023, Peoples R China
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2020年 / 41卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Minimal submanifold; Ejiri rigidity theorem; Ricci curvature; Mean curvature; PARALLEL MEAN-CURVATURE; MINIMAL SUBMANIFOLDS; SPHERE;
D O I：
10.1007/s11401-020-0199-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let M-n(n >= 4) be an oriented compact submanifold with parallel mean curvature in an (n + p)-dimensional complete simply connected Riemannian manifold Nn+p. Then there exists a constant delta(n, p) 2 (0, 1) such that if the sectional curvature of N satisfies, and if M has a lower bound for Ricci curvature and an upper bound for scalar curvature, then N is isometric to Sn+p. Moreover, M is either a totally umbilic sphere. This is a generalization of Ejiri's rigidity theorem.
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页码：285 / 302
页数：18
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