arXiv research

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Study on generalized quasi-Einstein structures in contact geometry.

The study finds quasi-Einstein metrics on sphere bundles.

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

The study classifies quasi-Einstein manifolds with boundary.

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

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

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…

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.

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…

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…

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

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

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 paper explores rigidity in conformal submersions and quasi-Einstein manifolds.

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

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…

Study curvature properties in special manifolds using specific tensors.

Study on rigidity of special Riemannian manifolds.

The study lifts certain Sasakian manifolds to quasi-Einstein spacetimes.

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…

The goal of this article is to study the geometry of Bach-flat noncompact steady quasi-Einstein manifolds. We show that a Bach-flat noncompact steady quasi-Einstein manifold $(M^{n},\,g)$ with positive Ricci curvature such that its potential function has at least one critical point must be a warped product with Einstei…

In this article we give a classification of three dimensional m-quasi Einstein manifolds with two distinct Ricci-eigen values. Our study provides explicit description of local and complete metrics and potential functions. We also describe the associated warped product Einstein manifolds in detail. For the proof we pres…

We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.

Killing fields on compact m-quasi-Einstein manifolds are shown under specific curvature conditions.

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…

The paper classifies compact quasi-Einstein manifolds with boundary.

The study extends and generalizes a result about quasi Einstein manifolds, proving conditions for Killing vector fields.

New findings on static near horizon geometries and quasi-Einstein manifolds, including rigidity results for negative cosmological constant.

The paper explores generalized quasi-Einstein manifolds and their properties.

New rigidity results for quasi-Einstein metrics with non-zero divergence-free vector fields.