We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel secon...We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.展开更多
In this paper,we study the complete space-like submanifold Mn with constant scalar curvature R≤c in the de Sitter space Spn+p(c) and obtain a pinching condition for Mn to be totally umbilical ones.The result generali...In this paper,we study the complete space-like submanifold Mn with constant scalar curvature R≤c in the de Sitter space Spn+p(c) and obtain a pinching condition for Mn to be totally umbilical ones.The result generalizes that in [5,Main Theorem] to higher codimension and give a complement for n=2 there.展开更多
Abstract： This paper concerns space-like submanifolds in a pseudo-Riemannianspace-time Sp^m＋p∪→Ep^m＋p＋1 （P ≥ 1）, and proves that connected compact maximalsuace-like submanifolds in a pseudo-Riemannian spaceti...Abstract： This paper concerns space-like submanifolds in a pseudo-Riemannianspace-time Sp^m＋p∪→Ep^m＋p＋1 （P ≥ 1）, and proves that connected compact maximalsuace-like submanifolds in a pseudo-Riemannian spacetime Sp^m＋p∪→Ep^m＋p＋1 （P ≥ 1） must be totally umbilical, and also totally geodesic. Particularly, when p = 1, our result is just Montiel＇s in case of H = 0.展开更多
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
The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We firs...The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized.展开更多
Complete space-like submanifolds in a de Sitter Space with parallel mean curvature vector are investigated, a main Theorem for M to be totally umbilical is obtained.
We study biharmonic submanifolds in δ-pinched Riemannian manifolds, and obtain some sufficient conditions for biharmonic submanifolds to be minimal ones.
Let M n be a complete space-like submanifold with parallel mean curvature vector in an indefinite space form N n+p p (c).A sharp estimate for the upper bound of the norm of the second fundamental form ...Let M n be a complete space-like submanifold with parallel mean curvature vector in an indefinite space form N n+p p (c).A sharp estimate for the upper bound of the norm of the second fundamental form of M n is obtained. A generalization of this result to complete space-like hypersurfaces with constant mean curvature in a Lorentz manifold is given. Moreover, harmonic Gauss maps of M n in N n+p p(c) in a generalized sense are considered.展开更多
This paper studied the conditions such that an n-dimensional complete space-like submanifold M with a parallel mean curvature vector field in an indefinite space form nppSc+()(p2,n3) is a totally umbilical submanifold...This paper studied the conditions such that an n-dimensional complete space-like submanifold M with a parallel mean curvature vector field in an indefinite space form nppSc+()(p2,n3) is a totally umbilical submanifold. By means of Laplacian estimation and the choice of a diagonal frame field, the following theorem is proved: if M is quasi-conformally flat and 2,HcRic(M)d?M1(1)轾--犏臌nt2()-cH, then M is a totally umbilical submanifold.展开更多
文摘We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.
文摘In this paper,we study the complete space-like submanifold Mn with constant scalar curvature R≤c in the de Sitter space Spn+p(c) and obtain a pinching condition for Mn to be totally umbilical ones.The result generalizes that in [5,Main Theorem] to higher codimension and give a complement for n=2 there.
文摘Abstract： This paper concerns space-like submanifolds in a pseudo-Riemannianspace-time Sp^m＋p∪→Ep^m＋p＋1 （P ≥ 1）, and proves that connected compact maximalsuace-like submanifolds in a pseudo-Riemannian spacetime Sp^m＋p∪→Ep^m＋p＋1 （P ≥ 1） must be totally umbilical, and also totally geodesic. Particularly, when p = 1, our result is just Montiel＇s in case of H = 0.
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.
文摘The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized.
文摘Complete space-like submanifolds in a de Sitter Space with parallel mean curvature vector are investigated, a main Theorem for M to be totally umbilical is 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.
文摘Let M n be a complete space-like submanifold with parallel mean curvature vector in an indefinite space form N n+p p (c).A sharp estimate for the upper bound of the norm of the second fundamental form of M n is obtained. A generalization of this result to complete space-like hypersurfaces with constant mean curvature in a Lorentz manifold is given. Moreover, harmonic Gauss maps of M n in N n+p p(c) in a generalized sense are considered.
基金the Outstanding Youth Foundation of China (No. 19925103)
文摘This paper studied the conditions such that an n-dimensional complete space-like submanifold M with a parallel mean curvature vector field in an indefinite space form nppSc+()(p2,n3) is a totally umbilical submanifold. By means of Laplacian estimation and the choice of a diagonal frame field, the following theorem is proved: if M is quasi-conformally flat and 2,HcRic(M)d?M1(1)轾--犏臌nt2()-cH, then M is a totally umbilical submanifold.
