Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

Abstract

We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

LP‐Kenmotsu Manifolds Admitting η‐Ricci Solitons and Spacetime

“…From ( 52) and (107), we obtain Λ � − 3 and ρ � 1. It is obvious that the metric g of an LP-Kenmotsu manifold satisfies the η-Ricci soliton equation (33), that is,…”

“…However, this is the beginning of dealing with η-Ricci solitons and spacetime physics. In the future, we will focus on studying various types of solitons in Lorentzian manifolds combined with singularity theory and submanifolds theory, presented in [11,12,20,25,[32][33][34][35] to obtain new results and theorems. Many problems of spacetime symmetries and Ricci soliton are still unresolved, and we hope that the readers of the present paper can do a good amount of work on the subject.…”

The Invariants of Dual Parallel Equidistant Ruled Surfaces

“…Finally, we provide an example for each of these indicatrix curves. It is possible to combine the results of this study with the concepts of submanifold theory or studies in other spaces and obtain new results [42][43][44][45][46][47].…”

Geometry of $\ast$-$k$-Ricci-Yamabe soliton and gradient $\ast$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

“…In [48], authors have considered * -Ricci solitons and gradient almost * -Ricci solitons on Kenmotsu manifolds and obtained some beautiful results. Very recently, Dey et al [13][14][15][16][17]29,30,34,38,41] have studied * -Ricci solitons and their generalizations in the framework of almost contact geometry. Recently D. Dey [11] introduced the notion of * -Ricci-Yamabe soliton ( * -RYS) as follows :…”