Ahmet Yildiz and Uday Chand De Dumlup\i nar University, University of Calcutta
Abstract : In this paper we study $h$-projectively semisymmetric, $\phi $-projectively semisymmetric, $h$-Weyl semisymmetric and $\phi $-Weyl semisymmetric non-Sasakian $(k,\mu )$-contact metric manifolds. In all the cases the manifold becomes an $\eta $-Einstein manifold. As a consequence of these results we obtain that if a $3$-dimensional non-Sasakian $(k,\mu )$-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an $N(k)$-contact metric manifold.
