On eta-Einstein N(k)-contact metric manifolds

Abstract

The aim of this paper is to characterize eta-Einstein N(k)-contact metric manifolds admits eta-Ricci soliton. Several consequences of this result are discussed. Beside these, we also study eta-Einstein N(k)-contact metric manifolds satisfying certain curvature conditions. Among others it is shown that such a manifold is either locally isometric to the Riemannian product En+1(0) Sn(4) or a Sasakian manifold. Finally, we construct an example to verify some results.