Study geometric properties and physical applications of mixed quasi-Einstein spacetime.
problem Characterize geometric and physical properties of mixed quasi-Einstein spacetime.
method Analyze geometric conditions and curvature tensors on mixed quasi-Einstein and nearly quasi-Einstein manifolds.
result Establish conditions for specific curvature tensors and spacetime structures.
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.
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 study explores properties of a specific type of spacetime.
problem Discussing geometric and physical properties of hyper-generalised quasi-Einstein spacetime.
method Analyzing various types of pseudosymmetry and Ricci symmetry over the spacetime.
result Proved the existence of a non-trivial hyper-generalised quasi-Einstein spacetime.
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.
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 study characterizes GRW spacetimes with gradient solitons and phantom era.
problem Characterizing generalized Robertson-Walker spacetimes with gradient solitons.
method Examined gradient type Ricci solitons and (m,τ)-quasi Einstein solitons in GRW spacetimes. result Demonstrated that GRW spacetimes can be Robertson-Walker or phantom era spacetimes under certain conditions.
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.
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 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.
Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.
problem Exploring geometric properties of Vaidya-Bonner-de Sitter spacetime.
method Analyzing conformal curvature, conharmonic curvature, and other curvatures.
result VBdS spacetime exhibits various pseudosymmetric structures and geometric features.
The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metric. It is shown that generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spaceti…
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.
The study characterizes spacetimes with specific solitons in f(R)-gravity.
problem Characterizing spacetimes with specific solitons in f(R)-gravity. method Analyzing η-Ricci solitons, gradient η-Ricci solitons, gradient Einstein Solitons, and gradient m-quasi Einstein solitons in perfect fluid spacetimes obeying f(R)-gravity. result Established conditions for the behavior of η-Ricci solitons and derived significant theorems about dark matter. We give necessary and sufficient conditions for warped product manifolds with 1-dimensional base, and in particular, for generalized Robertson-Walker spacetimes, to satisfy some generalized Einstein metric condition. We also construct suitable examples of such manifolds. They are quasi-Einstein or not.
The paper examines geometric properties of a specific black hole spacetime.
problem Curvature properties of a Hayward black hole spacetime.
method Analyzes the curvature properties of Hayward black hole spacetime using Einstein field equations.
result The Hayward black hole spacetime is an Einstein manifold and exhibits various types of pseudosymmetry.
Som-Raychaudhuri spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is …
The paper examines geometric properties of a unique spacetime model.
problem Investigating the geometric properties of a point-like global monopole spacetime.
method Analyzing the spacetime's pseudosymmetry structures, energy-momentum tensor, and curvature properties.
result The point-like global monopole spacetime exhibits various pseudosymmetry structures and properties.
The study examines perfect fluid spacetimes and their properties.
problem Characterizing properties of perfect fluid spacetimes with concircular vector fields.
method Analyzing the conformal curvature tensor, state equation, and solitons in perfect fluid spacetimes.
result Perfect fluid spacetimes with concircular vector fields have specific properties related to the state equation and solitons.
The paper studies geometric structures of wormholes using a new connection.
problem Exploring new geometric properties of wormholes.
method Extended Levi-Civita connection to semi-symmetric non-metric connections.
result Morris-Thorne wormholes exhibit specific geometric properties.
The charged Nariai spacetimes are the exact solutions of Einstein-Maxwell field equations with positive cosmological constant and such a spacetime is the direct topological product of a 2-dimentional de-Sitter spacetime with a round 2-sphere of constant radius. The present paper deals with the investigation of curv…
Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.
problem Proving the spacetime positive mass theorem for specific spacetime configurations.
method Solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.
result Established spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends.
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.
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.
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.
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 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.
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.
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 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 classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codim…
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.
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 …
Compact quasi-Einstein metrics with constant scalar curvature are locally homogeneous in 3D.
problem Characterize compact quasi-Einstein metrics with constant scalar curvature.
method Connection to Sasakian geometry and circle bundles over Einstein metrics.
result 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.
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 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.
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. 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…
A spacetime denotes a pure radiation field if its energy momentum tensor represents a situation in which all the energy is transported in one direction with the speed of light. In 1989, Wils and later in 1997 Ludwig and Edgar studied the physical properties of pure radiation metrics, which are conformally related to a …
The aim of this note is to give an explicit description of quasi-Einstein metrics on Hn×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.
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.
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.
Warped product manifolds with p-dimensional base, p=1,2, satisfy some curvature conditions of pseudosymmetry type. These conditions are formed from the metric tensor g, the Riemann-Christoffel curvature tensor R, the Ricci tensor S and the Weyl conformal curvature C of the considered manifolds. The main result of the p…
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 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 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.
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.