On N(k)-Contact Metric Manifolds

Abstract

The object of the present paper is to study a type of contact metric manifolds, called N(k)contact metric manifolds admitting a non-null concircular and torse forming vector field. Among others it is shown that such a manifold is either locally isometric to the Riemannian product E n+1 (0)× S n (4) or a Sasakian manifold. Also it is shown that such a contact metric manifold can be expressed as a warped product I×ep