The paper studies extended quasi-Einstein manifolds with special geometric properties and solitons.
problem Exploring new types of manifolds in general relativity.
method Generalization of existing manifolds and construction of specific examples.
result Existence and properties of extended quasi-Einstein manifolds with solitons.
The study characterizes mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.
problem Characterizing mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.
method Exploring properties of mixed super quasi-Einstein manifolds, including conformal Ricci pseudosymmetry and Einstein's field equation. Characterizing manifolds that admit Ricci-Bourguignon solitons and providing a detailed eigenvalue problem characterization.
result Characterization of mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons, including a detailed eigenvalue problem and an example construction.
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 introduces comprehensive quasi-Einstein spacetimes and explores their properties.
problem Exploring new types of spacetimes in general relativity.
method Mathematical analysis of geometric and physical properties of comprehensive quasi-Einstein manifolds.
result Existence of comprehensive quasi-Einstein spacetimes and their properties.
The paper studies geodesic mappings in special Riemannian manifolds.
problem Investigating geodesic mappings in specific Riemannian manifolds.
method Proof of geodesic mappings properties and new results on geodesic mappings of various Riemannian manifolds.
result New results on geodesic mappings of quasi Einstein, Ricci recurrent, and Ricci symmetric manifolds.
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…
The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.
problem Characterizing and analyzing pseudo generalized Ricci-recurrent spacetimes in modified gravity.
method Introducing and characterizing pseudo generalized Ricci-recurrent spacetimes, proving their properties, and studying their impact under modified gravity scenarios.
result Pseudo generalized Ricci-recurrent spacetimes represent specific spacetime types under modified gravity scenarios.
We call a metric m-quasi-Einstein if RicXm, 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…
Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
Paper defines semi-quasi-Einstein manifolds and applies to Schwarzschild and Kottler spacetimes.
problem Defining and studying semi-quasi-Einstein manifolds.
method Introduced from a semi symmetric metric connection, analyzed with curvature conditions and Killing generators.
result Schwarzschild and Kottler spacetimes exhibit semi-quasi-Einstein structure.
Study geometric inequalities for quasi-Einstein manifolds using new formulas.
problem Investigate geometric inequalities on quasi-Einstein manifolds.
method Use generalized Reilly's formulas and establish new boundary estimates and isoperimetric inequalities.
result Present a Heintze-Karcher type inequality for compact quasi-Einstein manifolds.
This paper proves certain quasi-Einstein manifolds are rigid under Ricci flow.
problem Understanding the behavior of quasi-Einstein metrics under Ricci flow.
method Employing a curvature evolution identity associated with Ricci flow.
result Certain closed quasi-Einstein manifolds are rigid under Ricci flow.
Study finds conditions for certain warped product manifolds to be quasi-Einstein.
problem Conditions for quasi-Einstein sequential warped product manifolds.
method Investigated necessary and sufficient conditions for specific types of manifolds.
result Identified conditions for sequential warped product manifolds to be quasi-Einstein.
Study on rigidity and characterization of generalized quasi-Einstein manifolds.
problem Rigidity and characterization of generalized quasi-Einstein manifolds.
method Analytical and geometric methods, including rigidity results and potential function analysis.
result Characterization of manifolds conformal to Euclidean space and explicit examples.
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…
Conformally quasi-recurrent (CQR)_n pseudo-Riemannian manifolds are investigated, and several new results are obtained. It is shown that the Ricci tensor and the gradient of the fundamental vector are Weyl compatible tensors (the notion was introduced recently by the authors and applies to significative space-times), (…
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 classifies quasi-Einstein manifolds with constant scalar curvature.
problem Characterizing quasi-Einstein manifolds with specific curvature properties.
method Classification and construction of examples of quasi-Einstein manifolds.
result Complete classification of quasi-Einstein manifolds with constant scalar curvature.
Study compact quasi-Einstein manifolds with boundary estimates.
problem Understanding boundary behavior of quasi-Einstein manifolds.
method Provide boundary estimates and prove isometric properties.
result Compact quasi-Einstein manifolds with connected boundary are isometric to the standard hemisphere.
Study on rigidity of special Riemannian manifolds.
problem Rigidity properties of generalized m-quasi-Einstein manifolds of Yamabe-type. method Investigation of rigidity properties for the potential vector field in compact and non-compact settings.
result The potential vector field either vanishes identically or becomes a non-trivial Killing vector field under certain assumptions.
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…
The paper classifies quasi-Einstein manifolds with harmonic Weyl curvature.
problem Classifying quasi-Einstein manifolds with specific curvature properties.
method Extending and refining previous work on quasi-Einstein manifolds, focusing on harmonic Weyl curvature.
result New examples of quasi-Einstein manifolds are provided, which are neither locally conformally flat nor D-flat.
The paper classifies quasi-Einstein 3-manifolds and their properties.
problem Classifying compact locally homogeneous non-gradient quasi-Einstein 3-manifolds.
method Analyzing quotient spaces of Lie groups and using properties of quasi-Einstein metrics.
result Identifies conditions for the existence of nontrivial quasi-Einstein metrics.
Study on quasi-Einstein manifolds with boundary estimates and inequalities.
problem Understanding the geometry of compact quasi-Einstein manifolds with boundary.
method Sharp boundary estimates and characterization theorems for quasi-Einstein manifolds.
result New geometric inequalities and boundary estimates for quasi-Einstein manifolds.
The paper studies m-quasi Einstein manifolds with convex potential and finds constant scalar curvature.
problem Investigating m-quasi Einstein manifolds with a convex potential function. method Analyzing integral conditions and properties of the potential vector field.
result An m-quasi Einstein manifold with a convex potential function has constant scalar curvature. The paper proves quasi-Einstein structures on manifolds admit Killing vector fields and provides new examples.
problem Classifying quasi-Einstein structures and understanding their properties.
method Analyzing quasi-Einstein equations and exploring their connections to Hitchin's equations.
result A class of quasi-Einstein structures on closed manifolds must admit a Killing vector field.
The study lifts certain Sasakian manifolds to quasi-Einstein spacetimes.
problem Understanding lifts of Sasakian manifolds to quasi-Einstein spacetimes.
method Analyzing smooth Sasakian manifolds and their lifts to 4D quasi-Einstein spacetimes.
result Smooth Sasakian manifolds can be lifted to quasi-Einstein shearfree spacetimes of Petrov type II or D.
The paper explores generalized quasi-Einstein manifolds and their properties.
problem Investigating properties of generalized quasi-Einstein manifolds under specific conditions.
method Analyzing natural conditions on potential vector fields and deriving consequences.
result The potential vector field is shown to be Killing under suitable integral assumptions.
The study of potential functions on noncompact quasi-Einstein manifolds, focusing on dimensions and flatness.
problem Characterizing potential functions on noncompact quasi-Einstein manifolds.
method Analyzing the dimensionality and structure of potential functions on specific manifolds.
result The dimension of positive potential functions on a three-dimensional noncompact quasi-Einstein manifold is at most two, with equality if and only if the manifold is a product of a λ-Einstein surface and R. The paper explores rigidity in conformal submersions and quasi-Einstein manifolds.
problem Understanding rigidity in conformal submersions and quasi-Einstein manifolds.
method Employing techniques involving conformal submersions to establish rigidity results.
result Established rigidity results for a class of closed quasi-Einstein manifolds with λ > 0.
The paper estimates the diameter of (m,ρ)-quasi Einstein manifolds under specific conditions.
problem Estimating the diameter of (m,ρ)-quasi Einstein manifolds. method Analyzing the properties of (m,ρ)-quasi Einstein manifolds and applying geometric and topological constraints. result An upper bound for the diameter of (m,ρ)-quasi Einstein manifolds is determined. The study finds quasi-Einstein metrics on sphere bundles.
problem Finding quasi-Einstein metrics on specific types of manifolds.
method Adapting Hall's work, the study explores quasi-Einstein metrics on sphere bundles over Fano Kaehler-Einstein manifolds and their blow-downs.
result The discovery of quasi-Einstein metrics on sphere bundles.
The study extends and generalizes a result about quasi Einstein manifolds, proving conditions for Killing vector fields.
problem Characterizing conditions for Killing vector fields in quasi Einstein manifolds.
method Extending and generalizing Cochran's result, proving conditions for Killing vector fields under specific integrals and conformal conditions.
result Conditions for Killing vector fields in quasi Einstein manifolds, including integral identities and global isometry to spheres.
The study classifies quasi-Einstein manifolds with boundary.
problem Classifying quasi-Einstein manifolds with boundary.
method Analyzing scalar curvature and isometric properties.
result Compact quasi-Einstein manifolds with boundary are rigid.
The study provides volume growth estimates for specific types of manifolds.
problem Estimating volume growth for Ricci solitons and quasi-Einstein manifolds.
method Similar to classical results, the study proves volume growth estimates for gradient Ricci solitons and quasi-Einstein manifolds.
result Sharp volume growth estimates for gradient shrinking Ricci solitons and upper bound volume growth estimates for quasi-Einstein manifolds.
The paper investigates (m,ρ)-quasi-Einstein structures on almost co-Kähler manifolds.
problem Investigating (m,ρ)-quasi-Einstein structures on almost co-Kähler manifolds. method Analyzing (m,ρ)-quasi-Einstein metrics on almost co-Kähler manifolds and studying their properties. result The paper proves that (m,ρ)-quasi-Einstein structures on almost co-Kähler manifolds are rare and have specific properties. The study examines a semi-symmetric metric connection in perfect fluid space-time and phantom barriers.
problem Investigating the properties of semi-symmetric metric connections in perfect fluid space-time.
method Using concircularly semi-symmetric metric connections, the study derives conditions for quasi-Einstein manifolds and examines the scalar curvature of perfect fluid space-times.
result The study proves that in a perfect fluid space-time, the scalar curvature is constant and represents a phantom barrier.
The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.
problem Characterizing and classifying manifolds with specific geometric properties.
method Analyzing warped products, contact manifolds, and semi-Riemannian manifolds.
result Characterizations and classifications of weakly conformally flat and quasi-Einstein manifolds.
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…
New findings on static near horizon geometries and quasi-Einstein manifolds, including rigidity results for negative cosmological constant.
problem Rigidity of quasi-Einstein manifolds under different cosmological constant conditions.
method Analysis of quasi-Einstein equations on closed manifolds, focusing on static vacuum solutions and their properties.
result For negative cosmological constant, rigidity holds under specific conditions on the 1-form \(X\), including incompressibility, constant norm, and nontrivial cohomology.
The study explores (m,ρ)-quasi-Einstein structures on contact metric manifolds.
problem Exploring (m,ρ)-quasi-Einstein structures in contact geometry. method Proving properties of (m,ρ)-quasi-Einstein structures on contact metric manifolds. result Compact contact or H-contact metric manifolds with (m,ρ)-quasi-Einstein structures have specific properties. Study on compact Quasi-Einstein manifolds yields diameter estimates and Hitchin-Thorpe inequality conditions.
problem Estimating diameters and verifying Hitchin-Thorpe inequality for compact Quasi-Einstein manifolds.
method Derive geometric estimates relating potential function oscillation to manifold diameter; derive lower bounds for diameter.
result Diameter conditions ensure compact Quasi-Einstein manifolds satisfy Hitchin-Thorpe inequality in dimension four.
In this short note we prove that any complete four dimensional anti-self-dual (or self-dual) quasi-Einstein manifolds is either Einstein or locally conformally flat. This generalizes a recent result of X. Chen and Y. Wang.
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 proves a spin manifold's 4D quasi-Einstein satisfies Hitchin-Thorpe inequality.
problem Proving a specific inequality for a class of 4D manifolds.
method Analyzing properties of gradient m-quasi-Einstein manifolds, focusing on spin structures. result Compact 4D spin gradient m-quasi-Einstein manifolds satisfy the Hitchin-Thorpe Inequality when m≥1. 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…
New rigidity results for quasi-Einstein metrics with non-zero divergence-free vector fields.
problem Classifying quasi-Einstein metrics with specific vector field properties.
method Analyzing quasi-Einstein metrics on closed manifolds and near-horizon geometries of extreme black holes.
result These metrics always admit a one-parameter group of isometries generated by the divergence-free vector field.
Study rigidifies non-compact manifolds with specific curvature conditions.
problem Analyzing non-compact generalized m-quasi-Einstein manifolds with constant scalar curvature and soliton function.
method Introduced a weighted function and proved its subharmonicity to derive rigidity results.
result Proves manifolds are Euclidean under specific conditions, with constant μ essential.