Generalized Ejiri’s Rigidity Theorem for Submanifolds in Pinched Manifolds(In memory of Professor Chaohao Gu on his 90th birthday)  

作　　者：Hongwei XU Li LEI Juanru GU 

机构地区：[1]Center of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China [2]Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310023,China

出　　处：《Chinese Annals of Mathematics,Series B》2020年第2期285-302,共18页数学年刊（B辑英文版）

基　　金：the National Natural Science Foundation of China(Nos.11531012,11371315,11301476)。

摘　　要：Let Mn(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 δ(n, p) ∈(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■ , a Clifford hypersurface Sm■ in the totally umbilic sphere ■, or■ . This is a generalization of Ejiri’s rigidity theorem.

关 键 词：Minimal SUBMANIFOLD Ejiri RIGIDITY theorem RICCI CURVATURE Mean CURVATURE 

分 类 号：O186.12[理学—数学]