On the contact conformal curvature tensor of a contact metric manifold

Abstract

The contact conformal curvature tensor of an N(kappa)-contact rhetric manifolds is studied. We prove that an N(kappa)-contact metric manifold with vanishing extended contact conformal curvature tensor is a Sasakian manifold. It is proved that a (2n + 1)-dimensional N(kappa)-contact metric manifold with non-vanishing contact conformal curvature tensor C-0 satisfies R(xi, X) . C-0 = 0 if and only if it is locally isometric to En+1 x S-n(4) for n > 1 and flat for n = 1. We also prove that the Ricci tensor S of an N(kappa)-contact metric manifold satisfies the condition C-0(xi, X) . S = 0 if and only if the manifold is 3-dimensional and flat.