A note on η-Ricci solitons in 3-dimensional trans-Sasakian manifolds

Abstract

In this paper we study η-Ricci soliton on 3-dimensional trans-Sasakian manifold. First we obtain the existence of η-Einstein soliton on  3-dimensional trans-Sasakian manifold. Next we establish some results on 3-dimensional trans-Sasakian manifold satisfying an η-Ricci soliton  when the manifold is Ricci-symmetric, has Codazzi or cyclic η-recurrent Ricci curvature tensor. Later we observe η-Ricci Soliton on 3-dimensional trans-Sasakian manifold satisfying the conditions t· S=0, S· t=0, M· S=0 and S· M=0. Also we construct an example of almost-η-Ricci soliton on 3-dimensional trans-Sasakian manifold