arXiv research

The paper proves quasi-Einstein structures on manifolds admit Killing vector fields and provides new examples.

The purpose of this article is to study the existence and uniqueness of quasi-Einstein structures on $3$-dimensional homogeneous Riemannian manifolds. To this end, we use the eight model geometries for 3-dimensional manifolds identified by Thurston. First, we present here a complete description of quasi-Einstein metric…

In this article, we study almost cosymplectic manifolds admitting quasi-Einstein structures $(g, V, m, λ)$. First we prove that an almost cosymplectic $(κ,μ)$-manifold is locally isomorphic to a Lie group if $(g, V, m, λ)$ is closed and on a compact almost $(κ,μ)$-cosymplectic manifold there do not exist quasi-Einstein…

The study explores $(m,ρ)$-quasi-Einstein structures on contact metric manifolds.

The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces. Quasi-Einstein metrics serve also as solution to the Ricci flow equation. Here, the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is …

Paper defines semi-quasi-Einstein manifolds and applies to Schwarzschild and Kottler spacetimes.

Study on generalized quasi-Einstein structures in contact geometry.

We investigate the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor. We show that if the Weyl tensor is harmonic and the potential function preserves this harmonicity then, in the isotropic case, the manifold is necessarily a $pp$-wave. Using the quasi-Einstein…

In this paper emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the generalized $m$-quasi-Einstein manifold, and vice versa. Considering a $n$-dimensional generalized $m$-quasi-Einstein manifold which is conformal to a pseudo-Euclidean space, we prove the most general symme…

The paper investigates $(m,ρ)$-quasi-Einstein structures on almost co-Kähler manifolds.

The paper proves a spin manifold's 4D quasi-Einstein satisfies Hitchin-Thorpe inequality.

The paper studies extended quasi-Einstein manifolds with special geometric properties and solitons.

New quasi-Einstein metrics found on a sphere.

Study geometric properties and physical applications of mixed quasi-Einstein spacetime.

In this paper we prove that under certain conditions in a quasi Einstein semi Riemannian warped product the fiber is necessarily a Einstein manifold. We provide all the quasi Einstein manifolds when r Bakry Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space invariant under the action…

In this paper, we study the quasi-Einstein and generalized quasi-Einstein warped products with a semi-symmetric non-metric connection. We give the expressions of the Ricci tensors and scalar curvatures for the bases and fibres. In some cases we give some obstructions to the existence of the quasi-Einstein and generaliz…

The study classifies quasi-Einstein manifolds with constant scalar curvature.

The paper classifies quasi-Einstein manifolds with harmonic Weyl curvature.

The study explores properties of a specific type of spacetime.

The paper introduces comprehensive quasi-Einstein spacetimes and explores their properties.

The paper classifies quasi-Einstein 3-manifolds and their properties.

Study geometric inequalities for quasi-Einstein manifolds using new formulas.

The study characterizes mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.

Study on quasi-Einstein manifolds with boundary estimates and inequalities.

Study new Einstein-like metrics and their properties.

The study finds quasi-Einstein metrics on sphere bundles.

This paper proves certain quasi-Einstein manifolds are rigid under Ricci flow.

Compact quasi-Einstein metrics with constant scalar curvature are locally homogeneous in 3D.

The paper studies $m$-quasi Einstein manifolds with convex potential and finds constant scalar curvature.

The aim of this paper is to present some structural equations for generalized quasi-Einstein metrics which was defined recently by Catino in [12]. In addition, supposing that the Riemannian manifold is Einstein we shall show that it is a space form with a well defined potential function f. Finally, we shall derive some…

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds simi\-lar to previous results obtained for static and $V$-static spaces. In addition, we show that compact quasi-Einstein manifolds with connected boundary and satisfyi…

The study of potential functions on noncompact quasi-Einstein manifolds, focusing on dimensions and flatness.

We call a metric quasi-Einstein if the $m$-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the construction of the warped product Einstein metrics. We study properties of quasi-Einst…

The aim of this note is to give an explicit description of quasi-Einstein metrics on $\Bbb{H}^{n}\times \Bbb{R}.$ We shall construct two examples of quasi-Einstein metrics on this manifold and then we shall prove the uniqueness of these examples. Finally, we shall describe the closed relation between quasi-Einstein met…

Study finds conditions for certain warped product manifolds to be quasi-Einstein.

We examine the space of solutions to the affine quasi--Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitions, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descript…

We provide classification results for and examples of half conformally flat generalized quasi Einstein manifolds of signature $(2,2)$. This analysis leads to a natural equation in affine geometry called the affine quasi-Einstein equation that we explore in further detail.

The paper estimates the diameter of $(m,ρ)$-quasi Einstein manifolds under specific conditions.

The study classifies quasi-Einstein manifolds with boundary.

Study on rigidity and characterization of generalized quasi-Einstein manifolds.

We call a metric $m$-quasi-Einstein if $Ric_X^m$, which replaces a gradient of a smooth function $f$ by a vector field $X$ in $m$-Bakry-Emery Ricci tensor, is a constant multiple of the metric tensor. It is a generalization of Einstein metrics which contains Ricci solitons. In this paper, we focus on left-invariant met…

In this paper we introduce the notion of generalized quasi--Einstein manifold, that generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold with harmonic Weyl tensor and with zero radial Weyl curvature, is locally a war…

The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.

We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature $(2,2)$ manifolds, to conformally Einstein manifolds and also to new Einstein manifolds through a warped product const…

Based on a well-known fact that there are no Einstein hypersurfaces in a non-flat complex space form, in this article we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hyersurface of a non-flat complex space form. For the real hypersurface with quasi-Einstein metric of …

The study provides volume growth estimates for specific types of manifolds.

Study on compact Quasi-Einstein manifolds yields diameter estimates and Hitchin-Thorpe inequality conditions.

We construct quasi-Einstein metrics on some hypersurface families. The hypersurfaces are circle bundles over the product of Fano, Kähler-Einstein manifolds. The quasi-Einstein metrics are related to various gradient Kähler-Ricci solitons constructed by Dancer and Wang and some Hermitian, non-Kähler, Einstein metrics co…