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.
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