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

• Published in: Frontiers in physics Vol. 10
• Main Authors: Dey, Santu, Turki, Nasser Bin
• Format: Journal Article
• Language: English
• Published: Frontiers Media S.A 10.02.2022
• Subjects: gradient almost ∗-η-Ricci soliton; para-Kenmotsu manifold; Ricci flow; η-Ricci soliton
• ISSN: 2296-424X; 2296-424X
• DOI: 10.3389/fphy.2022.809405

The goal of the present study is to study the ∗ -η-Ricci soliton and gradient almost ∗ -η-Ricci soliton within the framework of para-Kenmotsu manifolds as a characterization of Einstein metrics. We demonstrate that a para-Kenmotsu metric as a ∗ -η-Ricci soliton is an Einstein metric if the soliton vector field is contact. Next, we discuss the nature of the soliton and discover the scalar curvature when the manifold admits a ∗ -η-Ricci soliton on a para-Kenmotsu manifold. After that, we expand the characterization of the vector field when the manifold satisfies the ∗ -η-Ricci soliton. Furthermore, we characterize the para-Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies the gradient almost ∗ -η-Ricci soliton.