SOME NOTES ON KENMOTSU MANIFOLD

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In the present paper, we deal with a Kenmotsu manifold $M$. Firstly, we study the notion of torse-forming vector field on such a manifold. Then, we investigate some curvature conditions such as $Q.\mathcal{M}=0$ and $C.Q=0$ on such a manifold and obtain some necessary conditions for such a manifold given as to be Einstein and $\eta-$Einstein. Also, we study a Kenmotsu manifold $M$ admitting a Ricci soliton and give an example for this manifold.