We study the global umbilic submanifolds with parallel mean curvature vector fields in a Riemannian manifold with quasi constant curvature and get a local pinching theorem about the length of the second fundamental form.
The para-Blaschke tensor are extended in this paper from hypersurfaces to general higher codimensional submanifolds in the unit sphere S^(n),which is invariant under the Mobius transformations on Sn.Then some typical ...The para-Blaschke tensor are extended in this paper from hypersurfaces to general higher codimensional submanifolds in the unit sphere S^(n),which is invariant under the Mobius transformations on Sn.Then some typical new examples of umbilic-free submanifolds in Snwith vanishing Mobius form and a parallel para-Blaschke tensor of two distinct eigenvalues,D_(1) and D_(2),are constructed.The main theorem of this paper is a simple characterization of these newly found examples in terms of the eigenvalues D_(1) and D_(2).展开更多
基金Supported by the Directing Research Subject of Jiangsu Education Bureau(03103146)
文摘We study the global umbilic submanifolds with parallel mean curvature vector fields in a Riemannian manifold with quasi constant curvature and get a local pinching theorem about the length of the second fundamental form.
基金Supported by Foundation of Natural Sciences of China(Grant Nos.11671121,11871197,11431009)。
文摘The para-Blaschke tensor are extended in this paper from hypersurfaces to general higher codimensional submanifolds in the unit sphere S^(n),which is invariant under the Mobius transformations on Sn.Then some typical new examples of umbilic-free submanifolds in Snwith vanishing Mobius form and a parallel para-Blaschke tensor of two distinct eigenvalues,D_(1) and D_(2),are constructed.The main theorem of this paper is a simple characterization of these newly found examples in terms of the eigenvalues D_(1) and D_(2).
