On Some Classes of Generalized Quasi Einstein Manifolds

Abstract

In the present paper, we investigate generalized quasi Einstein manifolds satisfying some special curvature conditions R.S = 0, R.S = L_SQ(g; S), C.S = 0, C'. S = 0, W'. S = 0 and W_2. S = 0 where R, S, C, C', W' and W_2 respectively denote the Riemannian curvature tensor, Ricci tensor, conformal curvature tensor,
concircular curvature tensor, quasi conformal curvature tensor and W_2-curvature tensor. Later, we find some sucient conditions for a generalized quasi Einstein manifold to be a quasi Einstein manifold and we show the existence of a nearly quasi Einstein manifolds, by constructing a non trivial example.