Geometry of para-Sasakian metric as an almost conformal η-Ricci soliton

Abstract

In this paper, we initiate the study of conformal η-Ricci soliton and almost conformal η-Ricci soliton within the framework of para-Sasakian manifold. We prove that if para-Sasakian metric admits conformal η-Ricci soliton, then the manifold is η-Einstein and either the soliton vector field V is Killing or it leaves ϕ invariant. Here, we show the characteristics of the soliton vector field V and scalar curvature when the manifold admits conformal η-Ricci soliton and vector field is pointwise collinear with the characteristic vector field ξ. Next, we show that a para-Sasakian metric endowed an almost conformal η-Ricci soliton is η-Einstein metric if the soliton vector field V is an infinitesimal contact transformation. We also display that the manifold is Einstein if it represents a gradient almost conformal η-Ricci soliton. We develop an example to display the existence of conformal η-Ricci soliton on 3-dimensional para-Sasakian manifold.