Rigidity of closed submanifolds in a locally symmetric Riemannian manifold
Rigidity of closed submanifolds in a locally symmetric Riemannian manifold作者机构：Department of Applied Mathematics Zhejiang University of Technology Hangzhou 310023 China Center of Mathematical Sciences Zhejiang University Hangzhou 310027 China
出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)
年 卷 期：2016年第31卷第2期
页 面：237-252页
核心收录：
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金：Supported by the National Natural Science Foundation of China(11531012,11371315,11301476) the TransCentury Training Programme Foundation for Talents by the Ministry of Education of China the Postdoctoral Science Foundation of Zhejiang Province(Bsh1202060)
主 题：Submanifold Ejiri rigidity theorem Ricci curvature Mean curvature.
摘 要：Let Mn（n ≥ 4） be an oriented closed submanifold with parallel mean curvature in an （n ＋ p）-dimensional locally symmetric Riemannian manifold Nn＋p. We prove that if the sectional curvature of N is positively pinched in [5, 1], and the Ricci curvature of M satisfies a pinching condition, then M is either a totally umbilical submanifold, or δ= 1, and N is of constant curvature. This result generalizes the geometric rigidity theorem due to Xu and Gu [15].
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