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

Abstract

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

Keywords

• conformal η-ricci soliton
• kenmotsu manifold
• einstein manifold
• infinitesimal contact transformation
• para-cosymplectic manifold
• 53c15
• 53c25
• 53d15