Kenmotsu流形的不变子流形

IN VARIANT SUBMANIFOLDS OF A KENMOTSU MANIFOLD

主要对Kenmotsu流形的不变子流形和反不变子流形进行讨论,得到了以下两个主要结论:1.若M是具有常截面曲率C的Kenmotsu空间型(?)(C)的不变子流形,则M全测地的充要条件为M也具有常截面曲率C.2.若M^(n+1)是Kenmotsu流形M^(2n+1)的反不变子流形,则M的法联络平坦当且仅当M有常曲率C=-1.

In this paper. The following two main results was proued.i ) Let M be an invariant submanifolci of a Kcnrnotsu space form M ( C ) with constant -sectional curvature C.Then M is totally geodesic if and only if M is of constant -sectional curvature C.ii ) Let M be an (n+1)-dimensional anti-invariant submanifold, tangent to the structure vector field , of a (2n + l)-dimensional Kenmotsu manifoldM. Then the nornal connection of M is flat if and only if M is of constant curvature -i.