摘要
本文得到黎曼流形中的全脐子流形为共形平坦子流形的一个充要条件，并把[1]中的结论推广到Sasakian空间形式中去．
We first give the necessary and sufficient condition, on that a totally umbilical submanifolds in a Riemannian manifold is a conformally flat,Then we generalized the resulte in [1] over a Sasakian space form:Let M be a (2n+1)-dimensiona (n > 2) totally unbilical submanifold immersed in an m-dimensional (m > 3) Sasakian space form M(c), then M is conformally flat or it is totally geodesic.
关键词
Sasakian空间形式、全脐子流形
全脐不变子流形
常φ一截面曲率
Sasakian space form
Totally umbilical submanifold
Totally umbilical invariable submanifold
Constant φ-sectional curvature
