On N(k)-contact metric manifolds satisfying certain conditions

Abstract

We classify $N(k)$-contact metric manifolds satisfying the conditions $\sout{Z}(\xi ,X)\cdot C_0=0$, $C_0(\xi ,X)\cdot \sout{Z}=0$ and $C_e(\xi ,X)\cdot \sout{Z}=0$, where $\sout{Z},C_0$ and $C_e$ denote the concircular curvature tensor, the contact conformal curvature tensor and the extended contact conformal curvature tensor, respectively.