N(k)-contact metric manifolds with generalized Tanaka-Webster connection

Abstract

In this paper, we characterize N(k)-contact metric manifolds with generalized Tanaka-Webster connection. We obtain some curvature properties. It is proven that if an N(k)-contact metric manifold with generalized Tanaka-Webster connection is K-contact then it is an example of generalized Sasakian space form. Also, we examine some flatness and symmetric conditions of concircular curvature tensor on an N(k)-contact metric manifolds with generalized Tanaka-Webster connection.

Some Curvature Tensor Relations on Nearly Cosymplectic Manifolds with Tanaka-Webster Connection

“…Many authors have studied the Tanaka-Webster connection later. In relation to the generalized Tanaka-Webster connection Ghosh, Prakasha, Ünal and Montano have done important studies on this connection in various structures [13,[19][20][21]. We, on the other hand, tried to define some curvature tensors on nearly cosymplectic structures according to the tanaka webster connection, taking into account some previous studies.…”