云南民族大学学报（自然科学版）2017，Vol.26Issue(3)：212-215,240,5.DOI:12.3969/j.issn.1672-8513.2017.03.009
球面上κ-极值子流形的Pinching定理
A Pinching theorem for k-extremal submanifolds in a sphere
摘要
Abstract
Let Mn be a n-dimensional compact κ-extremal submanifolds(1 ≤κ ＜ n/2) in a unit sphere Sn+P(n ≥3),it is proved that if (∫Mnρdv)2/n ＜ C,then |A |2 =nH2 and are a totally umbilical,where only depends on n,ρ,Mn.Set ρ2 =|A |2-nH2,H and |A|2 and respectively denote the mean curvature and the squared length of the second fundamental form of Mn.关键词
κ-极值子流形/Pinching定理/紧致/Sobolev不等式Key words
κ-extremal submanifolds/Pinching theorem/compact/Sobolev inequality分类
数理科学引用本文复制引用
米蓉,刘建成..球面上κ-极值子流形的Pinching定理[J].云南民族大学学报（自然科学版）,2017,26(3):212-215,240,5.基金项目
国家自然科学基金(11261051) （11261051）
甘肃省高等学校基本科研业务费资助项目. （）
