Some results on N(k)-contact metric manifolds

M. Altin, H. İ. Yoldaş, I. Ünal

In this study, some geometric properties of N(k)-contact metric manifolds, which are important class of contact manifolds, have been investigated by using a special connection (CY-connection). First, we give some fundamental results on N(k)-contact metric manifolds admitting CY-connection. Then, we obtain curvature properties of such manifolds. We prove that an N(k)-contact metric manifold admitting R*(ξ,X).R*=0 condition is an N(-1/4)-contact metric manifold, where R* is the Riemannian curvature tensor of CY-connection. Also, we examine an N(k)-contact metric manifold admitting CY-connection under W*(ξ,X).S*=0 condition for generalized quasi-conformal curvature tensor W* of CY-connection. Finally, we consider a 3-dimensional N(k)-contact metric manifold admitting CY-connection.

Advanced Studies: Euro-Tbilisi Mathematical Journal, Special Issue (10 - 2021), pp. 83-97