复射影空间中全实平行平均曲率子流形的拼挤定理  

Pinching Theorem for Totally Real Submanifolds with Parallel Mean Curvature in the Complex Projective Space

作　　者：关莉 许洪伟 赵恩涛 GUAN Li;XU Hongwei;ZHAO Entao(Center of Mathematical Sciences,Zhejiang University,Hangzhou,Zhejiang,310027,P.R.China)

机构地区：[1]浙江大学数学科学研究中心,杭州浙江310027

出　　处：《数学进展》2022年第5期931-940,共10页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.11531012,12071424)。

摘　　要：设M是全纯截面曲率为4的复射影空间CP~(n+p)中的n维完备全实平行平均曲率子流形.对于x∈M,令τ(x)=max_(u,v∈U_xM,u⊥v)‖h(u,u)-h(v,v)‖^(2),其中U_(x)M={u∈T_(x)M;‖u‖=1},T_(x)M是M在x处的切空间,h表示M的第二基本形式.我们证明,若τ(x)≤4/3,x∈M,那么或者τ≡0且M是全脐的,或者τ≡4/3.Let M be an n-dimensional complete totally real submanifold with parallel mean curvature in the complex projective space CP^(n+p) of holomorphic sectional curvature 4.For x∈M,setτ(x)=max_(u,v∈U_xM,u⊥v)‖h(u,u)-h(v,v)‖^(2),where U_(x)M={u∈T_(x)M;‖u‖=1},TxM is the tangent space at x∈M and h denotes the second fundamental form of M.We prove that ifτ(x)≤4/3 for all x∈M,then eitherτ≡0 and M is totally umbilical,orτ≡4/3.

关 键 词：复射影空间 全实子流形 平行平均曲率 刚性定理 

分 类 号：O186.12[理学—数学]