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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]

The main goal of this manuscript is to investigate the properties of N(k)-contact metric manifolds admitting a Z*-tensor. We prove the necessary conditions for which N(k)- contact metric manifolds endowed with a Z*-tensor are Einstein manifolds. In this sequel, we accomplish that an N(k)-contact metric manifold endowed with a Z*-tensor satisfying Z*(G1, ζ).R* = 0 is either locally isometric to the Riemannian product En+1(0)×Sn(4) or an Einstein manifold. We also prove the condition for which an N(k)-contact metric manifold endowed with a Z*-tensor is a Sasakian manifold. To validate some of our results, we construct a non-trivial example of an N(k)-contact metric manifold. [ABSTRACT FROM AUTHOR]

Warped products provide an elegant and versatile framework for exploring and understanding a wide range of geometric structures. Their ability to combine two distinct manifolds through a warping function introduces a rich and diverse set of geometries, thus making them a powerful tool in various mathematical, physical, and computational applications. This article addresses the central query related to warped product submanifolds in the context of statistics. It focuses on deriving two new and distinct inequalities for a statistical warped product submanifold in a statistical manifold of a constant (quasi-constant) curvature. This article then finishes with some concluding remarks. [ABSTRACT FROM AUTHOR]

This paper characterizes the Lorentzian manifolds endowed with a semi-symmetric non-metric ρ -connection (briefly, ssnmρc). First, the existence of semi-symmetric non-metric connection (ssnmc) on Lorentzian manifold is established, and it is shown that an n -dimensional Lorentzian manifold equipped with an ssnmρc is a generalized Robertson–Walker spacetime. We also establish the condition for a Lorentzian manifold together with an ssnmρc to be a Robertson–Walker spacetime. In this series, the properties of Ricci semi-symmetric Lorentzian manifold endowed with an ssnmρc, almost Ricci solitons and gradient Ricci solitons are explored. Finally, a non-trivial example of Lorentzian manifold admits an ssnmρc, which is constructed to verify some of our results. [ABSTRACT FROM AUTHOR]

We characterize N(k)-paracontact metric manifolds (NKPMM) M2n+1 satisfying the Fischer-Marsden conjecture. We demostrate that, if an M2n+1 satisfies the Fischer-Marsden equation, then either M2n+1 with k > -1 is a non-Einstein manifold or M2n+1 is locally isometric to En+1 Hn(-4) for n > 1. For the 3-dimensional case, we show that M³ is an Einstein manifold. [ABSTRACT FROM AUTHOR]

This paper aims to explore the metallic structure J 2 = p J + q I , where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle T M over almost quadratic ϕ -structures (briefly, (ϕ , ξ , η) ). Tensor fields F ˜ and F * are defined on T M , and it is shown that they are metallic structures over (ϕ , ξ , η) . Next, the fundamental 2-form Ω and its derivative d Ω , with the help of complete lift on T M over (ϕ , ξ , η) , are evaluated. Furthermore, the integrability conditions and expressions of the Lie derivative of metallic structures F ˜ and F * are determined using complete and horizontal lifts on T M over (ϕ , ξ , η) , respectively. Finally, we prove the existence of almost quadratic ϕ -structures on T M with non-trivial examples. [ABSTRACT FROM AUTHOR]

The target of the current research article is to investigate the solitonic attributes of relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci–Yamabe soliton (RY-soliton) and gradient Ricci–Yamabe soliton (GRY-soliton). We exhibit that a magneto-fluid spacetime filled with a magneto-fluid density ρ , magnetic field strength H, and magnetic permeability μ obeys the Einstein field equation without the cosmic constant being a generalized quasi-Einstein spacetime manifold (G Q E) . In such a spacetime, we obtain an EoS with a constant scalar curvature R in terms of the magnetic field strength H and magnetic permeability μ. Next, we achieve some cauterization of the magneto-fluid spacetime in terms of Ricci–Yamabe solitons with a time-like torse-forming vector field ξ and a φ (R i c) vector field. We establish the existence of a black hole in the relativistic magneto-fluid spacetime by demonstrating that it admits a shrinking Ricci–Yamabe soliton and satisfies the time-like energy convergence criteria. In addition, we examine the magneto-fluid spacetime with a gradient Ricci–Yamabe soliton and deduce some conditions for an equation of state (EoS) ω = − 1 5 with a Killing vector field. Furthermore, we demonstrate that the EoS ω = − 1 5 of the magneto-fluid spacetime under some constraints represents a star model and a static, spherically symmetric perfect fluid spacetime. Finally, we prove that a gradient Ricci–Yamabe soliton with the conditions μ = 0 or H = 2 ; μ ≠ 0 , H > 2 and obeying the equation of state ω = − 1 5 is conceded in a magneto-fluid spacetime, and a naked singularity with a Cauchy horizon subsequently emerges, respectively. [ABSTRACT FROM AUTHOR]

Purpose - The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, λ-Ricci solitons and three-dimensional weakly Z symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional proper trans-Sasakian manifold. Design/methodology/approach - The authors have used the tensorial approach to achieve the goal. Findings - A second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g. Originality/value - The authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication. [ABSTRACT FROM AUTHOR]

This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field of the quasi-Yamabe soliton is of gradient type c = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate η-Einstein solitons on (ε)-Kenmotsu manifolds when the Weyl-conformal curvature tensor satisfies some geometric properties such as being flat, semi-symmetric and Einstein semi-symmetric. Here, we discuss the properties of η-Einstein solitons on φ-symmetric (ε)-Kenmotsu manifolds. [ABSTRACT FROM AUTHOR]

The aim of this article is to study the h-almost Ricci solitons and h-almost gradient Ricci solitons on generalized Sasakian-space-forms. First, we consider h-almost Ricci soliton with the potential vector field V as a contact vector field on generalized Sasakian-space-form of dimension greater than three. Next, we study h-almost gradient Ricci solitons on a three-dimensional quasi-Sasakian generalized Sasakian-space-form. In both the cases, several interesting results are obtained. [ABSTRACT FROM AUTHOR]

This paper deals with the study of a special class of almost contact metric manifold, called trans-Sasakian manifold. We also study the properties of the Ricci solitons in generalized recurrent, Weyl semisymmetric, Einstein semisymmetric, Weyl pseudo symmetric and partially Ricci pseudo symmetric trans-Sasakian manifolds. Example of trans-Sasakian manifold is given in the last section to validate our results. [ABSTRACT FROM AUTHOR]