In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decre...In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decrease.展开更多
Let x be an m-dimensional umbilic-free hypersurface in an （m＋1）-dimensional unit sphere Sm＋l （m≥3）. In this paper, we classify and explicitly express the hypersurfaces with two distinct princi- pal curvatures a...Let x be an m-dimensional umbilic-free hypersurface in an （m＋1）-dimensional unit sphere Sm＋l （m≥3）. In this paper, we classify and explicitly express the hypersurfaces with two distinct princi- pal curvatures and closed MSbius form, and then we characterize and classify conformally flat hypersurfaces of dimension larger than 3.展开更多
文摘In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decrease.
基金supported by National Natural Science Foundation of China (Grant Nos.10561010, 10861013)
文摘Let x be an m-dimensional umbilic-free hypersurface in an （m＋1）-dimensional unit sphere Sm＋l （m≥3）. In this paper, we classify and explicitly express the hypersurfaces with two distinct princi- pal curvatures and closed MSbius form, and then we characterize and classify conformally flat hypersurfaces of dimension larger than 3.
