Kenmotsu流形的半不变子流形

Semi-Invariant Submanifold of Kenmotsu Manifold

给出了Kenmotsu流形的子流形成为半不变积的两个充要条件 ,即 :1)设M是Kenmotsu流形M的半不变子流形 ,则M为M的半不变积的充要条件为 :对任意Y∈Γ(TM) ,X ∈Γ(D) ,有 XY∈Γ(D { ξ} ) .2 )设M是Kenmotsu流形M的半不变子流形 ,则M为M的半不变积的充要条件是 :对任意X∈Γ(TM) ,Y∈Γ(D) ,有fB(X ,Y) =0 .

Mainly, we botain two sufficient and necessary conditions of submanifold becoming semi invariant products of Kenmotsu manifolds. That is, ⅰ) Let M be a semi invariant submanifold of a Kenmotsu manifold M . Then M is a semi invariant product if and only if\-yX∈Γ(D{ξ}), for any Y∈Γ(TM) and X∈Γ(D) ⅱ) Let M be a semi invariant submanifold of a Kenmotsu manifold. Then M is a semi invariant product if and only if fB(X, Y)=0, of any X∈Γ(TM) and Y∈Γ(D)