∗-η-Ricci Soliton and Gradient Almost ∗-η-Ricci Soliton Within the Framework of Para-Kenmotsu Manifolds - Dey, Santu; Turki, Nasser Bin (Frontiers in Physics, 2022)
The goal of the present paper is to deliberate *-η-Ricci soliton and gradient almost *-η-Ricci soliton within the framework of para-Kenmotsu manifolds as a characterization of Einstein metrics. Here we display that a para-Kenmotsu metric as a *-η-Ricci soliton is Einstein metric if the soliton vector field is contact. Next, we have displayed the nature of the soliton and discover the scalar curvature when the manifold admitting *-η-Ricci soliton on para-Kenmotsu manifold. After that, we have grown the characterization of the vector field when the manifold satisfies *-η-Ricci soliton. Furthermore, we have developed the characterization of the para-Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost *-η-Ricci soliton. Then, we have studied gradient *-η-Ricci soliton to yield the nature of Riemannian curvature tensor and characterization of potential vector field on para-Kenmotsu manifold. Lastly, we decorate an example of *-η-Ricci soliton, gradient almost *-η-Ricci soliton on para-Kenmotsu manifold to prove our findings.