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 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.
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.
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 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 …
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 quasi-Einstein metrics on real hypersurfaces of complex space forms.
problem No Einstein metrics in non-flat complex space forms, explore quasi-Einstein condition.
method Analyze real hypersurfaces in complex Euclidean space, classify quasi-Einstein metrics.
result Classify quasi-Einstein metrics on real hypersurfaces of complex Euclidean space.
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.
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…
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…
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…
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 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…
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. The paper examines properties of generalized τ-quasi Ricci-harmonic metrics and proves rigidity results.
problem Characterizing and proving rigidity of generalized τ-quasi Ricci-harmonic metrics.
method Exploring conditions for harmonic-Einstein metrics, obtaining rigidity results, and proving gap theorems.
result Rigidity results for compact generalized τ-quasi Ricci-harmonic metrics.
Proves formula for unique Kähler-Einstein metric on quasi-projective manifolds.
problem Finding unique Kähler-Einstein metrics on quasi-projective manifolds.
method Elementary proof using ODE solutions and spectral theory.
result Asymptotic expansion formula for unique complete Kähler-Einstein metric.
We call a metric m-quasi-Einstein if RicXm (a modification of the m-Bakry-Emery Ricci tensor in terms of a suitable vector field X) 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 vector fields and…
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.
We present a general numerical method for investigating prescribed Ricci curvature problems on toric Kähler manifolds. This method is applied to two generalisations of Einstein metrics, namely Ricci solitons and quasi-Einstein metrics. We begin by recovering the Koiso--Cao soliton and the Lü--Page--Pope quasi-Einstein …
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 paper classifies Lie groups with specific quasi-Einstein metrics.
problem Investigating Lie groups with quasi-Einstein metrics.
method Complete classification of nilpotent and unimodular solvable Lie groups.
result Classification of Lie groups admitting quasi-Einstein metrics.
Study solutions to affine quasi-Einstein equation on homogeneous surfaces.
problem Understanding solutions to affine quasi-Einstein equation on homogeneous surfaces.
method Using the dimension of affine Killing vector fields as a framework, we provide explicit descriptions of solution spaces.
result Very explicit descriptions of solution spaces for gradient Yamabe solitions, conformally Einstein metrics, and warped product Einstein manifolds.
We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We use this formulation to give a sharp upper bound on the dimension of the vector …
Study new Einstein-like metrics and their properties.
problem Characterize a new class of quasi-Einstein metrics.
method Investigate modified Ricci solitons and their relationships.
result Prove rigidity of standard spheres under specific conditions.
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 Kähler-Einstein metrics on quasi-projective manifolds.
problem Constructing and analyzing Kähler-Einstein metrics on quasi-projective manifolds.
method Utilizes singular Kähler-Einstein metrics and conic Kähler-Einstein metrics of negative curvature.
result Established the weak convergence of conic Kähler-Einstein metrics to singular Kähler-Einstein metrics.
Smooth metric measure spaces have been studied from the two different perspectives of Bakry-Émery and Chang-Gursky-Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Ei…
New quasi-Einstein metrics found on a sphere.
problem Finding quasi-Einstein metrics on a sphere.
method Constructing axi-symmetric non-gradient m-quasi-Einstein structures using hypergeometric functions. result Found new regular metrics on a two-sphere, including the extreme Kerr black hole horizon.
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. We define Discrete Quasi-Einstein metrics (DQE-metrics) as the critical points of discrete total curvature functional on triangulated 3-manifolds. We study DQE-metrics by introducing some combinatorial curvature flows. We prove that these flows produce solutions which converge to discrete quasi-Einstein metrics when th…
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.
Classifies smooth metric measure spaces with two weighted Einstein representatives.
problem Classifying smooth metric measure spaces with specific weighted Einstein properties.
method Local and global classification using Einstein and quasi-Einstein warped products.
result Global classification result for complete manifolds, showing specific types of manifolds.
We prove that an admissible manifold (as defined by Apostolov, Calderbank, Gauduchon and Tønnesen-Friedman), arising from a base with a local Kähler product of constant scalar curvature metrics, admits Generalized Quasi-Einstein Kähler metrics (as defined by D. Guan) in all "sufficiently small" admissible Kähler classe…
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.
We prove that the quasi-Einstein metrics found by Lü, Page and Pope on CP1-bundles over Fano Kähler-Einstein bases are conformally Kähler and that the Kähler class of the conformal metric is a multiple of the first Chern class. A detailed study of the lowest-dimensional example of such metrics on $\mathbb…
Researchers develop weighted GJMS operators for smooth metric measure spaces.
problem Developing mathematical tools for smooth metric measure spaces.
method Constructing and proving formal self-adjointness of weighted GJMS operators.
result Formal self-adjointness of weighted GJMS operators proved.
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 examines flatness conditions on normal metric contact pairs and proves properties of Einstein manifolds.
problem The study of flatness conditions on normal metric contact pairs.
method Analysis of conformal, concircular, and quasi-conformal curvature tensors.
result Normal metric contact pair manifolds with flat conformal, concircular, and quasi-conformal curvature tensors are Einstein manifolds with specific scalar and sectional curvatures.
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 abstract discusses transforming Vaisman metrics into Kähler-Einstein structures.
problem Transforming Vaisman metrics into Kähler-Einstein structures.
method Using the transverse Kähler-Ricci flow on the canonical foliation of a closed Vaisman manifold.
result Direct proof of short time existence of transverse Kähler-Ricci flow on Vaisman manifolds.
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 paper defines a new connection on sub-Riemannian manifolds and explores conditions for almost quasi-Sasakian manifolds to be Einstein.
problem Exploring new connections and conditions for specific types of manifolds.
method Defining a skew-symmetric connection and studying its properties on sub-Riemannian manifolds, and examining conditions for almost quasi-Sasakian manifolds to be Einstein.
result Sufficient conditions are found for an almost quasi-Sasakian manifold to be an Einstein manifold.
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…
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.
Study investigates hypersurfaces in space forms satisfying a curvature condition.
problem Curvature condition for hypersurfaces in space forms.
method Investigates hypersurfaces in space forms N satisfying a specific curvature condition involving tensors.
result Main result states that if the curvature tensor of a non-quasi-Einstein hypersurface is a linear combination of Q(g,C) and Q(S,C), then the curvature condition (A) holds on M.
The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein metrics are unstable. By exploiting the relationship between warped product Einstei…
We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping funct…
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.