Classifications of $K$-Contact Semi-Riemannian Manifolds

Abstract

The object of the present paper is to characterize a K-contact semi-Riemannian manifold satisfying certain curvature conditions. We study Ricci semi-symmetric K-contact semi-Riemannian manifolds and obtain an equivalent condition. Next we prove that a K-contact semi-Riemannian manifold is of harmonic conformal curvature tensor if and only if the manifold is an Einstein manifold. Also we study $\xi$-conformally flat K-contact semi-Riemannian manifolds. Finally, we charecterize conformally semisymmetric Lorentzian $K$-contact manifolds.