Almost conformal Ricci soliton and η-Ricci soliton on 3-dimensional (ε, δ) trans-Sasakian manifold

Abstract

In this paper, we have shown that if a 3-dimensional (ε, δ) trans-Sasakian manifold admits conformal Ricci soliton (g, V, λ) and the vector field V is point-wise collinear with the unit vector field ξ then V is a constant multiple of ξ. Similarly, we have proved that under the same condition an almost conformal Ricci soliton becomes a conformal Ricci soliton. We have also studied η-Ricci soliton on (ε, δ) trans-Sasakian manifold. Finally, we have shown that if a 3-dimensional (ε, δ) trans-Sasakian manifold admits conformal gradient shrinking Ricci soliton then the manifold is an Einstein manifold.