In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 6634 （H2 114785 respectively） must be compact. Speciall...In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 6634 （H2 114785 respectively） must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4（-1） （resp. H5（-1）） with constant mean curvature H satisfying H2 6643 （resp. H2 114785 ） must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].展开更多
In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the...In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.展开更多
基金supported by NSFC (10901067)partially supported by NSFC (10801058) and Hubei Key Laboratory of Mathematical Sciences
文摘In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 6634 （H2 114785 respectively） must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4（-1） （resp. H5（-1）） with constant mean curvature H satisfying H2 6643 （resp. H2 114785 ） must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].
文摘In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.
