AUTHOR=Dey Santu , Turki Nasser Bin 

TITLE=∗-η-Ricci Soliton and Gradient Almost ∗-η-Ricci Soliton Within the Framework of Para-Kenmotsu Manifolds

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.809405

DOI=10.3389/fphy.2022.809405

ISSN=2296-424X

ABSTRACT=The goal of the present paper is to deliberate $*$-$\eta$-Ricci soliton and gradient almost $*$-$\eta$-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 $*$-$\eta$-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 $\ast$-$\eta$-Ricci soliton on para-Kenmotsu manifold. After that, we have grown the characterization of the vector field when the manifold satisfies $\ast$-$\eta$-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 $*$-$\eta$-Ricci soliton. Then, we have studied gradient $\ast$-$\eta$-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 $*$-$\eta$-Ricci soliton, gradient almost $*$-$\eta$-Ricci soliton  on para-Kenmotsu manifold to prove our findings.