Journal of the
Korean Mathematical Society JKMS

We classify $N(\kappa)$-contact metric manifolds which satisfy $Z(\xi,X)\cdot Z=0$, $Z(\xi,X)\cdot R=0$ or $R(\xi,X)\cdot Z=0$.

Keywords: contact metric manifold, $N(\kappa)$-contact metric manifold, $(\kappa,\mu)$-manifold, Sasakian manifold, concircular curvature tensor, concircularly symmetric, recurrent concircular curvature tensor

MSC numbers: 53C25, 53D10