∗-η-Ricci soliton and contact geometry

In the present paper, we initiate the study of ∗-η-Ricci soliton within the framework of Kenmotsu manifolds as a characterization of Einstein metrics. Here we display that a Kenmotsu metric as a ∗-η-Ricci soliton is Einstein metric if the soliton vector field is contact. Further, we have developed the characterization of the Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost ∗-η-Ricci soliton. Next, we deliberate ∗-η-Ricci soliton admitting (κ,μ)′-almost Kenmotsu manifold and proved that the manifold is Ricci flat and is locally isometric to Hn+1(-4)×Rn. Finally we present some examples to decorate the existence of ∗-η-Ricci soliton, gradient almost ∗-η-Ricci soliton on Kenmotsu manifold.