Certain results of conformal and *-conformal Ricci soliton on para-cosymplectic and para-Kenmotsu manifolds

Abstract

The goal of the paper is to deliberate conformal Ricci soliton and *-conformal Ricci soliton within the framework of paracontact geometry. Here we prove that if an ?-Einstein para-Kenmotsu manifold admits conformal Ricci soliton and *-conformal Ricci soliton, then it is Einstein. Further we have shown that 3-dimensional para-cosymplectic manifold is Ricci flat if the manifold satisfies conformal Ricci soliton where the soliton vector field is conformal. We have also constructed some examples of para-Kenmotsu manifold that admits conformal and *-conformal Ricci soliton and verify our results.