Let M be a connected n dimensional space form spacelike isometrically immersed in a (2n-1) dimensional indefinite space form. If M is maximal, we prove that either M is totally geodesic or M is a piece of the n ...Let M be a connected n dimensional space form spacelike isometrically immersed in a (2n-1) dimensional indefinite space form. If M is maximal, we prove that either M is totally geodesic or M is a piece of the n dimensional hyperbolic cylinder in the (2n-1) dimensional pseudo hyperbolic space. 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
基金the National Natural Science Foundationof China (No.1970 10 17
文摘Let M be a connected n dimensional space form spacelike isometrically immersed in a (2n-1) dimensional indefinite space form. If M is maximal, we prove that either M is totally geodesic or M is a piece of the n dimensional hyperbolic cylinder in the (2n-1) dimensional pseudo hyperbolic space.
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.
