$ N(\kappa)- $contact Metric Manifolds with Generalized Tanaka-Webster Connection

Abstract

In this paper we work on $ N(\kappa)- $contact metric manifolds with a generalized Tanaka-Webster connection . We obtain some curvature properties. It is proven that if a $ N(\kappa)- $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 a $ N(\kappa)- $contact metric manifolds with a generalized Tanaka-Webster connection.