The GJMS operators of special Einstein products are factored into simpler operators and applied to solve the Q-Yamabe problem.
problem Factorization of GJMS operators in special Einstein products.
method Factorization of GJMS operators as a composition of second- and fourth-order differential operators.
result The Green's function for the GJMS operator of order 2k is positive for certain special Einstein products.
Study on special warped product manifolds with Einstein metrics.
problem Characterizing Einstein metrics in specific warped product manifolds.
method Derive general formulas and prove existence of solutions for invariant families.
result Existence of families of solutions invariant under transformations for positive constant Ricci curvature.
The paper examines conditions for Einstein multiply warped products and estimates their parameters.
problem Existence and non-existence of non-trivial Einstein multiply warped products.
method Analyzes conditions for the existence or non-existence of Einstein multiply warped products, especially generalized Kasner type.
result Estimates the Einstein parameter that conditions the existence of such metrics.
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 study pseudo-Riemannian Einstein manifolds which are conformally equivalent with a metric product of two pseudo-Riemannian manifolds. Particularly interesting is the case where one of these manifolds is 1-dimensional and the case where the conformal factor depends on both manifolds simultaneously. If both factors ar…
Proves a special type of submanifolds in a curved space.
problem Characterizing submanifolds with specific properties in a curved space.
method Uses the properties of flat normal bundle and parallel mean curvature to prove the submanifolds are warped products.
result Einstein submanifolds with flat normal bundle and parallel mean curvature are warped product of isometric immersions.
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 paper studies special warped products with a specific connection on super Riemannian manifolds.
problem Investigating curvature and Ricci tensors on super warped product spaces with a semi-symmetric non-metric connection.
method Defined a semi-symmetric non-metric connection, computed curvature and Ricci tensors, and introduced and analyzed two types of super warped product spaces.
result Conditions for two super warped product spaces with a semi-symmetric non-metric connection to be Einstein spaces are provided.
New examples found of complex manifolds with special metrics.
problem Existence of Kähler-Einstein metrics on certain complex manifolds.
method Using Hultgren's polytope formulation, constructing explicit examples of toric Fano manifolds.
result Found examples of projective bundles that admit coupled Kähler-Einstein metrics but no ordinary Kähler-Einstein metrics.
New manifold type PNDP-manifold defined with Einstein warped product structure.
problem Defining manifolds with non-standard dimensions.
method Einstein warped product manifold with special base and fiber structures.
result PNDP-manifolds are Einstein warped product manifolds with specific base and fiber properties.
The study finds invariant Einstein metrics on complex Stiefel manifolds and special unitary groups.
problem Existence of invariant Einstein metrics on complex Stiefel manifolds and special unitary groups.
method Decomposing Lie algebras and tangent spaces, parametrizing scalar products, and computing Ricci tensors for invariant metrics.
result Existence of invariant Einstein metrics on specific special unitary groups and complex Stiefel manifolds.
It is an important problem in differential geometry to find non-naturally reductive homogeneous Einstein metrics on homogeneous manifolds. In this paper, we consider this problem for some coset spaces of compact simple Lie groups. A new method to construct invariant non-naturally reductive Einstein metrics on normal ho…
Study variational problem on manifold with special distributions.
problem Generalize Einstein metrics on manifold with multiple distributions.
method Define functional of pseudo-Riemannian metric and contorsion tensor, prove critical pairs make distributions totally umbilical.
result Metrics in critical pairs make all distributions totally umbilical.
Defines a new tensor related to special geometric spaces.
problem Understanding new curvature tensors in semi-Riemannian geometry.
method Defines a generalized curvature tensor using specific operations.
result The tensor is connected to quasi-Einstein, Roter, and Roter-type spaces.
The paper proves rigidity properties of holomorphic isometries into homogeneous Kähler manifolds.
problem Rigidity of holomorphic isometries into homogeneous Kähler manifolds.
method Analyzing Kähler-Ricci solitons, flat spaces, and homogeneous bounded domains.
result Strong extensions of rigidity results in previous studies.
Einstein metrics on products are shown to be warped.
problem Characterizing Einstein metrics on conformal products.
method Proving Einstein metrics on conformal products are warped products under natural geometric conditions.
result Einstein metrics on conformal products are proven to be warped products.
Study Einstein warped products with Einstein base and fiber.
problem Characterize Einstein warped products with Einstein base and fiber.
method Investigate necessary and sufficient conditions for a warped product to be Einstein.
result Explicitly determine the warping function when the base is hyperbolic space.
The study examines Einstein-Finsler spaces using Minkowskian products.
problem Characterizing Einstein-Finsler spaces through Minkowskian products.
method Proving conditions for Einstein-Finsler spaces in terms of Minkowskian products.
result If a Minkowskian product Finsler manifold is Einstein, then either the product manifold is Ricci flat or both quotient manifolds are Einstein with same scalar functions.
The paper presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds.
problem The challenge is to define the Einstein connection for nonsymmetric pseudo-Riemannian manifolds.
method The approach involves using a weak almost contact structure and a linear connection with torsion.
result Explicit formulas for the Einstein connection are provided.
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.
Study characterizes Einstein metrics in warped product spaces.
problem Characterizing Einstein metrics in warped product spaces.
method Local characterizations and global restatements of known results.
result Restated global characterizations of Einstein manifolds.
We introduce the concept of a base conformal warped product of two pseudo-Riemannian manifolds. We also define a subclass of this structure called as a special base conformal warped product. After, we explicitly mention many of the relevant fields where metrics of these forms and also considerations about their curvatu…
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…
Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first give a systematic presentation of the main geometric constructions, with emphasis…
The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.
problem Characterizing Einstein doubly warped product manifolds with a semi-symmetric metric connection.
method Deriving curvature formulas and proving necessary and sufficient conditions for a manifold to be a warped product.
result Obtained results for Einstein doubly warped product manifolds and Einstein-like doubly warped product manifolds.
Defines and computes a generalized spectral action for Lorentz warped products.
problem Computing spectral actions for Lorentz warped products.
method Defines and computes the bimetric spectral Einstein-Hilbert action for Lorentz warped products.
result Derives a Kastler-Kalau-Walze type theorem for Lorentz warped products.
The paper studies Einstein-type structures in warped product manifolds.
problem Characterizing Einstein-type structures in warped product manifolds.
method Analyzing conditions for minimal, totally umbilical, and geodesic immersions.
result Characterization of rotational hypersurfaces in RimesfRn. 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 paper examines gradient ρ-Einstein solitons on specific manifolds and spacetimes.
problem Characterizing gradient ρ-Einstein solitons on doubly warped product manifolds.
method Analyzing necessary and sufficient conditions for doubly warped product manifolds to be gradient ρ-Einstein solitons, applying results to specific spacetime models.
result No 3-dimensional essentially conformally symmetric gradient ρ-Einstein soliton exists.
In this article we study homogeneous warped product Einstein metrics and its connections with homogeneous Ricci solitons. We show that homogeneous (λ,n+m)-Einstein manifolds (which are the bases of homogeneous warped product Einstein metrics) are one-dimensional extensions of algebraic solitons. This answers a questi…
Study classifies Einstein spaces and warped products in weighted geometry.
problem Characterizing geometric structures of weighted Einstein spaces.
method Complete local classification of weighted Einstein spaces with harmonic Weyl tensor.
result Spaces decompose into Einstein or specific warped products.
Study Einstein warped-product manifolds with specific curvature conditions.
problem Understanding Einstein warped-product manifolds with screened Poisson equation constraints.
method Analyzing manifolds with specific curvature conditions and solving the screened Poisson equation.
result Dimension, Ricci curvature, and screened parameter are related through a quadratic equation.
We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kahler-Einstein manifolds. We compute the associated conformal invariants, i…
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…
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.
The paper presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds with specific torsion conditions.
problem Tackles the Einstein connection in nonsymmetric pseudo-Riemannian manifolds with non-degenerate skew-symmetric tensor.
method Explicitly presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds with f2-torsion condition. result Reduces to M.Prvanović's solution in the almost Hermitian case.
In this paper we show that a compact warped product Einstein manifold with vanishing Bach tensor of dimension n≥4 is a finite quotient of a warped product with (n−1)-dimensional Einstein fiber. The fiber has constant curvature if n=4.
New examples of weakly Einstein conformal products are constructed.
problem Classifying weakly Einstein conformal products.
method Established classification results and constructed new examples.
result No proper weakly Einstein manifolds have harmonic curvature.
The study of special metrics in various parabolic geometries.
problem Finding special metrics in parabolic geometries.
method Investigating invariant conditions for special metrics in different parabolic geometries.
result Characterization of special metrics in hypersurface CR and contact Legendrean cases.
Study Einstein Lie groups and geodesic orbit manifolds, finding some are not geodesic orbit.
problem Characterizing Einstein Lie groups and geodesic orbit manifolds.
method Characterizing GimesK-invariant geodesic orbit metrics on Lie groups G for regular subgroups K. result Extensive classes of compact simple Einstein Lie groups are not geodesic orbit manifolds.
The paper studies Einstein-Hilbert action on complex manifolds.
problem Deriving equations for the Einstein-Hilbert action on almost k-product manifolds. method Adapted variations of metric, deriving Euler-Lagrange equations.
result Presented a nice form of Einstein equation.
New result on Einstein manifolds using conformal product structures.
problem Understanding Einstein metrics on product manifolds.
method Generalizing previous results on Einstein metrics on product manifolds to conformal product structures.
result Einstein metrics on conformal product structures of compact manifolds are also warped product metrics.
Classifies vacuum static spaces with harmonic curvature.
problem Classifying vacuum static spaces with harmonic curvature.
method Thorough classification through geometric analysis.
result Spaces are locally isometric to four types.
We prove that complete warped product Einstein metrics with isometric bases, simply connected space form fibers, and the same Ricci curvature and dimension are isometric. In the compact case we also prove that the warping functions must be the same up to scaling, while in the non-compact case there are simple examples …
The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the approach of quasi-Einstein manifolds which is directly related to Einstein warped…
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the base is three dimensional and the dimension of the fiber is greater than one we sho…
New families of Ricci solitons found with collapsing volume.
problem Finding new Ricci solitons with specific volume behavior.
method Reduced soliton equation to Monge-Ampère equation coupled with ODEs.
result Explicit complete expanding solitons and existence results for other types.
In this paper we prove a number of triviality results for Einstein warped products and quasi-Einstein manifolds using different techniques and under assumptions of various nature. In particular we obtain and exploit gradient estimates for solutions of weighted Poisson-type equations and adaptations to the weighted sett…