In this paper we obtain some formulas for totally umbilical submanifolds in a localiy symmetric manifold, and dcrivc some local rcsults on the submanifolds from these formulas.
In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension...In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension is large enough.展开更多
The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions...The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation on its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat.展开更多
In this paper the quasi-constant curvature space and the Riemannian manifold contained the totally umbilical hypersurface family are studied,and two theorems are given at the same time.
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.
In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental f...In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental form and the mean curvature. We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval.This improved the relative results of M. Okumura,Shen Yibihg and Sun Ziqi,etc.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In this paper we obtain some formulas for totally umbilical submanifolds in a localiy symmetric manifold, and dcrivc some local rcsults on the submanifolds from these formulas.
文摘In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension is large enough.
文摘The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation on its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat.
文摘In this paper the quasi-constant curvature space and the Riemannian manifold contained the totally umbilical hypersurface family are studied,and two theorems are given at the same time.
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.
文摘In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental form and the mean curvature. We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval.This improved the relative results of M. Okumura,Shen Yibihg and Sun Ziqi,etc.
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.
