A Normal Paracontact Metric Manifold Satisfying Some Conditions on the $M$-Projective Curvature Tensor

Abstract

In the present paper we have studied the curvature tensors of a normal paracontact metric manifold satisfying the conditions $R(\xi,Y)W^{*}=0$, $W^{*}(\xi,Y)R=0$, $W^{*}(\xi,Y)\widetilde{Z}=0$, $W^{*}(\xi,Y)S=0$ and $W^{*}(\xi,Y)\widetilde{C}=0$, where $W^{*}$,$R$, $S$, $\widetilde{Z}$ and $\widetilde{C}$ are the $M$-projective curvature, Riemannian curvature, Ricci, concircular curvature and quasi-conformal curvature tensor, respectively.