An optimal rigidity theorem for complete submanifolds in a sphere

被引：0
|
作者：
Xu Hong-wei [1 ]
Zhu Jiao-feng [1 ]
机构：
[1] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Peoples R China
来源：
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B | 2008年 / 23卷 / 02期
基金：
中国国家自然科学基金;
关键词：
submanifold; rigidity; flat normal bundle; mean curvature;
D O I：
10.1007/s11766-008-0212-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is proved that if M-n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in Sn+p(1), and if sup(M) S < alpha(n, H), where alpha(n, H) = n + n(3)/2(n - 1) H-2 - n(n - 2)/2(n - 1) root n(2) H-4 + 4(n - 1)H-2, then M-n must be the totally umbilical sphere S-n (1/root 1+H-2). An example to show that the pinching constant alpha(n, H) appears optimal is given.
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页码：219 / 226
页数：8
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