Abstract
We prove that if an
-Einstein para-Kenmotsu manifold admits a conformal
-Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal
-Ricci soliton is Einstein if its potential vector field
is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal
-Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal
-Ricci soliton and satisfy our results. We also have studied conformal
-Ricci soliton in three-dimensional para-cosymplectic manifolds.