Conformal η-Ricci almost solitons of Kenmotsu manifolds

Abstract

The aim of this paper is to find some important classes of Einstein manifolds using conformal [Formula: see text]-Ricci solitons and conformal [Formula: see text]-Ricci almost solitons. We prove that a Kenmotsu metric as conformal [Formula: see text]-Ricci soliton is Einstein if it is [Formula: see text]-Einstein or the potential vector field [Formula: see text] is infinitesimal contact transformation or collinear with the Reeb vector field [Formula: see text]. Next, we prove that a Kenmotsu metric as gradient conformal [Formula: see text]-Ricci almost soliton is Einstein if the Reeb vector field leaves the scalar curvature invariants. Finally, we construct some examples to illustrate the existence of conformal [Formula: see text]-Ricci soliton, gradient almost conformal [Formula: see text]-Ricci soliton on Kenmotsu manifold.