Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

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