黎曼流形的B子流形

TOTALLY UMBILICAL SUBMANIFOLDS OF A RIEMANN MANIFOLD

通过考察一类特殊的A子流形,给出了非极小伪脐子流形成为全脐子流形的一个充要条件,得到了黎曼流形的子流形成为全脐子流形的两个充分条件及其它一些结果。

By studying a special class of A-submanifolds named B-submanifolds, we give a necessary and sufficient condition for a non-minimal pseudo-umbilical submanifold to be totally umbilical. We also obtain two sufficient conditions for a submanifold of a riemann manifold to be totally umbilical. Some other results are also presented.