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...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.展开更多
We study biharmonic submanifolds in δ-pinched Riemannian manifolds, and obtain some sufficient conditions for biharmonic submanifolds to be minimal ones.
基金Supported by the NNSF of China(71061012)Supported by the Young Talents Project of Dingxi Teacher's College(2012-2017)
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant No10871138)
文摘We study biharmonic submanifolds in δ-pinched Riemannian manifolds, and obtain some sufficient conditions for biharmonic submanifolds to be minimal ones.
