GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE  

作　　者：潘鹏飞 许洪伟 赵恩涛 Pengfei PAN;Hongwei XU;Entao ZHAO(Center of Mathematical Sciences,Zhejiang University,Hangzhou,310027,China;Yuanpei college,Shaoxing University,Shaoxing,312000,China)

机构地区：[1]Center of Mathematical Sciences,Zhejiang University,Hangzhou,310027,China [2]Yuanpei college,Shaoxing University,Shaoxing,312000,China

出　　处：《Acta Mathematica Scientia》2023年第1期169-183,共15页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11531012,12071424,12171423);the Scientific Research Project of Shaoxing University(2021LG016)。

摘　　要：In this paper,we mainly study the global rigidity theorem of Riemannian submanifolds in space forms.Let Mn(n≥3)be a complete minimal submanifold in the unit sphere Sn+p(1).Forλ∈[0,n2−1/p),there is an explicit positive constant C(n,p,λ),depending only on n,p,λ,such that,if∫MSn/2dM<∞,∫M(S−λ)n/2+dM<C(n,p,λ),then Mn is a totally geodetic sphere,where S denotes the square of the second fundamental form of the submanifold and∫+=max{0,f}.Similar conclusions can be obtained for a complete submanifold with parallel mean curvature in the Euclidean space Rn+p.

关 键 词：Euclidean space the unit sphere submanifolds with parallel mean curvature global rigidity theorem 

分 类 号：O186.12[理学—数学]