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 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.
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 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 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 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.
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.
Study on pp-waves in isotropic quasi-Einstein manifolds.
problem Characterizing the local structure of quasi-Einstein manifolds.
method Analysis of Weyl tensor properties and quasi-Einstein equation.
result Isotropic quasi-Einstein manifolds with harmonic Weyl tensor are pp-waves. 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 examines quasi-Einstein structures on specific types of manifolds.
problem Characterizing quasi-Einstein structures on almost cosymplectic manifolds.
method Analyzes properties of quasi-Einstein structures on almost cosymplectic manifolds, Lie groups, and K-cosymplectic manifolds.
result Closed quasi-Einstein structures on compact almost cosymplectic manifolds do not exist.
Study classifies half conformally flat GQE manifolds of signature (2,2).
problem Classifying half conformally flat generalized quasi-Einstein manifolds.
method Analysis and examples provided.
result Natural affine quasi-Einstein equation derived.
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. 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.
New types of Einstein manifolds discovered from homogeneous surfaces.
problem Understanding quasi-Einstein equations on homogeneous surfaces.
method Modified Riemannian extension and warped product construction.
result Discovery of new 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 on noncompact steady quasi-Einstein manifolds with positive Ricci curvature.
problem Characterize noncompact steady quasi-Einstein manifolds with positive Ricci curvature.
method Analyze Bach-flat noncompact steady quasi-Einstein manifolds with positive Ricci curvature, proving they must be warped products with Einstein fibers.
result Warped product structure with constant curvature for 4-dimensional manifolds.
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.
Authors classify 3D m-quasi Einstein manifolds with degenerate Ricci tensor.
problem Classifying 3D m-quasi Einstein manifolds with degenerate Ricci tensor.
method Using Codazzi tensor and geometric properties of the tensor to analyze m-quasi Einstein equation.
result Explicit description of local and complete metrics and potential functions.
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. 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.
The paper analyzes symmetry groups of a specific type of manifold.
problem Understanding the symmetry groups of generalized m-quasi-Einstein manifolds. method Analyzing a n-dimensional generalized m-quasi-Einstein manifold conformal to a pseudo-Euclidean space. result Proves the most general symmetry group of maximal dimension and shows no different low-dimensional invariants.
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.
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.
The study proves conditions for quasi-Einstein manifolds with specific structures to be Einstein.
problem Conditions for quasi-Einstein manifolds to have Einstein structures.
method Proved conditions for quasi-Einstein semi-Riemannian warped products to have Einstein fibers.
result Found conditions for quasi-Einstein manifolds with specific structures to be Einstein.
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.
This study classifies noncompact quasi-Einstein manifolds conformal to Euclidean spaces.
problem Investigating nontrivial quasi-Einstein manifolds globally conformal to Euclidean spaces.
method Considering manifolds with invariant conformal factors and potential functions under an (n−1)-dimensional translation group. result Complete classification of manifolds when λ=0 and m≥1 or m=2−n. 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. Study on noncompact steady quasi-Einstein manifolds with specific tensor conditions.
problem Classifying noncompact steady quasi-Einstein manifolds with vanishing Weyl tensor condition.
method Analyzing manifolds with nonnegative Ricci curvature and zero radial Weyl curvature under fourth-order divergence-free Weyl tensor condition.
result Proves that such manifolds must be a warped product with (n−1)−dimensional Einstein fiber. 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.
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…
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.
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.
Study quasi-Einstein metrics on cohomogeneity-one manifolds.
problem Find quasi-Einstein metrics on specific manifolds.
method Investigate G-invariant quasi-Einstein metrics on G/Himes(0,1) with monotypic conditions. result Estimate blow-up rates and find metrics satisfying Dirichlet conditions.
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. Study curvature properties in special manifolds using specific tensors.
problem Investigate curvature conditions in 2-quasi-Einstein manifolds.
method Analyze Riemann-Christoffel curvature tensor and its linear combinations with Ricci tensor.
result Satisfy pseudosymmetry type curvature conditions in certain manifolds.
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.
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.
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 study approximates Ricci solitons and quasi-Einstein metrics on toric surfaces.
problem Investigate Ricci solitons and quasi-Einstein metrics on toric Kähler manifolds.
method General numerical method applied to toric Kähler manifolds, focusing on two generalizations of Einstein metrics.
result Numerical approximations and solutions found for specific metrics on toric surfaces.
Killing fields on compact m-quasi-Einstein manifolds are shown under specific curvature conditions.
problem Characterizing Killing fields on compact m-quasi-Einstein manifolds.
method Extending a result by Bahuaud-Gunasekaran-Kunduri-Woolgar, the approach involves proving the existence of Killing fields under certain curvature conditions.
result A sufficient condition for a compact, non-gradient m-quasi-Einstein metric to admit a Killing field is provided, extending the original result to the m = -2 case.
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.
The paper classifies compact quasi-Einstein manifolds with boundary.
problem Classifying compact quasi-Einstein manifolds with boundary.
method Analyzing manifolds with nonnegative sectional curvature and zero radial Weyl tensor.
result Classification of quasi-Einstein manifolds, including standard hemisphere and new examples.