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In this study, we characterize LP-Kenmotsu manifolds admitting *-Ricci-Yamabe solitons (*-RYSs) and gradient *-Ricci-Yamabe solitons (gradient *-RYSs). It is shown that an LP-Kenmotsu manifold of dimension n admitting a *-Ricci-Yamabe soliton obeys Poisson's equation. We also determine the necessary and sufficient conditions under which the Laplace equation is satisfied by LP-Kenmotsu manifolds. Finally, by using a non-trivial example of an LP-Kenmotsu manifold, we verify some results of our paper. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate perfect fluid spacetimes and perfect fluid generalized Roberston-Walker spacetimes that contain a torse-forming vector field satisfying almost hyperbolic Ricci solitons. We show that the perfect fluid spacetimes that contain a torse-forming vector field satisfy an almost hyperbolic Ricci soliton, and we prove that a perfect fluid generalized Roberston-Walker spacetime satisfying an almost hyperbolic Ricci soliton (g, ζ, ..., µ) is an Einstein manifold. Also, we study an almost hyperbolic Ricci soliton (g, V, ..., µ) on these spacetimes when V is a conformal vector field, a torse-forming vector field, or a Ricci bi-conformal vector field. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of Riemannian warped-twisted product submersions and examine their fundamental properties, including total geodesicity, total umbilicity and minimality. Additionally, we investigate the Ricci tensor of Riemannian warped-twisted product submersions, specifically about the horizontal and vertical distributions. Finally, we obtain Einstein condition for base manifold if the horizontal and vertical distributions of the ambient manifold is Einstein. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize a Riemannian 3-manifold M 3 equipped with a semi-symmetric metric ξ -connection ∇ ˜ with ρ -Einstein and gradient ρ -Einstein solitons. The existence of a gradient ρ -Einstein soliton in an M 3 admitting ∇ ˜ is ensured by constructing a non-trivial example, and hence some of our results are verified. By using standard tensorial technique, we prove that the scalar curvature of (M 3 , ∇ ˜) satisfies the Poisson equation Δ R = 4 (2 − σ − 6 ρ) ρ . [ABSTRACT FROM AUTHOR]

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with - η -Ricci solitons. First we find some necessary conditions for such a manifold to be φ -Einstein. Then, we study the notion of - η -Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results. [ABSTRACT FROM AUTHOR]

In this paper, we characterize three-dimensional Riemannian manifolds M 3 admitting Ricci–Yamabe solitons (RYSs). It is proved that if an M 3 endowed with a semi-symmetric metric ζ -connection admits an RYS, then the scalar curvature of M 3 satisfies the Poisson equation Δ r = 8 (2 α − 3 β − ϱ) β , where α , β ∈ ℝ and β ≠ 0. We also discuss the existence of gradient RYS in Riemannian setting. Finally, we construct a nontrivial example of three-dimensional Riemannian 3-manifolds admitting RYS to prove some of our results. [ABSTRACT FROM AUTHOR]

In the present paper, we characterize m-dimensional ζ -conformally flat L P -Kenmotsu manifolds (briefly, (L P K) m ) equipped with the Ricci–Yamabe solitons (RYS) and gradient Ricci–Yamabe solitons (GRYS). It is proven that the scalar curvature r of an (L P K) m admitting an RYS satisfies the Poisson equation Δ r = 4 (m − 1) δ { β (m − 1) + ρ } + 2 (m − 3) r − 4 m (m − 1) (m − 2) , where ρ , δ (≠ 0) ∈ R . In this sequel, the condition for which the scalar curvature of an (L P K) m admitting an RYS holds the Laplace equation is established. We also give an affirmative answer for the existence of a GRYS on an (L P K) m . Finally, a non-trivial example of an L P -Kenmotsu manifold (L P K) of dimension four is constructed to verify some of our results. [ABSTRACT FROM AUTHOR]

In the present article, some geometric and physical properties of M G (Q E) n were investigated. Moreover, general relativistic viscous fluid M G (Q E) 4 spacetimes with some physical applications were studied. Finally, through a non-trivial example of M G (Q E) 4 spacetime, we proved its existence. [ABSTRACT FROM AUTHOR]

In this paper, we study the properties of ϵ -Kenmotsu manifolds if its metrics are * η -Ricci-Yamabe solitons. It is proven that an ϵ -Kenmotsu manifold endowed with a * η -Ricci-Yamabe soliton is η -Einstein. The necessary conditions for an ϵ -Kenmotsu manifold, whose metric is a * η -Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence * η -Ricci-Yamabe solitons. [ABSTRACT FROM AUTHOR]

In the present note, we study ϵ -LP-Sasakian 3-manifolds M 3 ϵ whose metrics are conformal η -Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M 3 ϵ with a constant scalar curvature admits a CERYS, then £ U ζ is orthogonal to ζ if and only if Λ − ϵ σ = − 2 ϵ l + m r / 2 + 1 / 2 p + 2 / 3 . Further, we study gradient CERYS in M 3 ϵ and proved that an M 3 ϵ admitting gradient CERYS is a generalized conformal η -Einstein manifold; moreover, the gradient of the potential function is pointwise collinear with the Reeb vector field ζ. Finally, the existence of CERYS in an M 3 ϵ has been drawn by a concrete example. [ABSTRACT FROM AUTHOR]

We characterize ∊-Kenmotsu manifolds admitting *-conformal η-Ricci solitons. At last, an example of 7-dimension ∊-Kenmotsu manifold is given. [ABSTRACT FROM AUTHOR]