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Pseudo-umbilical Biharmonic Submanifolds in Constant Curvature Spaces

Pseudo-umbilical Biharmonic Submanifolds in Constant Curvature Spaces
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摘要 The conjecture [1] asserts that any biharmonic submanifold in sphere has constant mean curvature. In this paper, we first prove that this conjecture is true for pseudo-umbilical biharmonic submanifolds M n in constant curvature spaces S n+p (c)(c > 0), generalizing the result in [1]. Secondly, some sufficient conditions for pseudo-umbilical proper biharmonic submanifolds M n to be totally umbilical ones are obtained. The conjecture [1] asserts that any biharmonic submanifold in sphere has constant mean curvature. In this paper, we first prove that this conjecture is true for pseudo-umbilical biharmonic submanifolds Ms in constant curvature spaces Sn＋P（c）（c 〉 0）, generalizing the result in [1]. Secondly, some sufficient conditions for pseudo-umbilical proper biharmonic submanifolds Ms to be totally umbilical ones are obtained.
作者 DU Li ZHANG Juan
机构地区 Department of Mathematics
出处 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第3期432-438,共7页 数学季刊（英文版）
基金 Supported by the NNSF of China(71061012) Supported by the Young Talents Project of Dingxi Teacher's College(2012-2017)
关键词 constant curvature spaces PSEUDO-UMBILICAL proper biharmonic submanifolds constant curvature spaces pseudo-umbilical proper biharmonic submanifolds
分类号 O186.16 [理学—基础数学]
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共引文献2

Chinese Quarterly Journal of Mathematics
2012年 第3期

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