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 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
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
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.
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.
