ON BIHARMONIC HYPERSURFACES WITH CONSTANT SCALAR CURVATURES IN S5

被引：7
|
作者：
Fu, Yu [1 ]
机构：
[1] Dongbei Univ Finance & Econ, Sch Math & Quantitat Econ, Dalian 116025, Peoples R China
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 143卷 / 12期
基金：
中国博士后科学基金;
关键词：
Biharmonic maps; biharmonic submanifolds; Chen's conjecture; Generalized Chen's conjecture; SUBMANIFOLDS;
D O I：
10.1090/proc/12677
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that proper biharmonic hypersurfaces with constant scalar curvature in Euclidean sphere S-5 must have constant mean curvature. Moreover, we also show that there exist no proper biharmonic hypersurfaces with constant scalar curvature in Euclidean space E-5 or hyperbolic space H-5, which give affirmative partial answers to Chen's conjecture and the Generalized Chen's conjecture.
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页码：5399 / 5409
页数：11
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