The Structure of Some Classes of Contact Metric Manifolds

Abstract

We study the conformal curvature tensor and the contact conformal curvature tensor in Sasakian and/or K-contact manifolds. We find a necessary and sufficient condition for a Sasakian manifold to be φ-conformally flat. We also find some necessary conditions for a K-contact manifold to be φ-contact conformally flat. Then we give a structure theorem for φ-contact conformally flat Sasakian manifolds. It is also proved that a Sasakian manifold cannot be ξ-contact conformally flat.