arXiv research

Characterizes warping functions in Einstein Poisson warped spaces.

Study Einstein warped products with Einstein base and fiber.

Study characterizes Einstein metrics in warped product spaces.

Study on Einstein warped spaces with specific connections and curvature properties.

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 …

Study classifies Einstein spaces and warped products in weighted geometry.

Study finds conditions for certain warped product manifolds to be quasi-Einstein.

Classifies smooth metric measure spaces with two weighted Einstein representatives.

The study constructs gradient Einstein-type warped metrics and proves nonexistence and rigidity results.

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. We obtain a uniqueness result for prescribing the Ricci curvatur…

Defines semi-symmetric metric connection on super warped products.

The paper studies Einstein hypersurfaces in a specific warped product space.

We study Einstein's equation in $(m+n)D$ and $(1+n)D$ warped spaces $(\bar{M},\bar{g})$ and classify all such spaces satisfying Einstein equations $\bar{G}=-\barΛ\bar{g}$. We show that the warping function not only can determine the cosmological constant $\barΛ$ but also it can determine the cosmological constant $Λ$ a…

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…

The paper studies special warped products with a specific connection on super Riemannian 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…

In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an Einstein one-dimensional extension if the soliton derivation can be chosen to be normal. Using our previous work on warped product Einstein metrics, we show that…

In this paper we consider a class of Einstein warped product semi-Riemannian manifolds $\widehat{M} = M^{n}\times_{f}N^{m}$ with $n\geq 3$ and $m\geq 2$. For $\widehat{M}$ with compact base and Ricci-flat fiber, we prove that $\widehat{M}$ is simply a Riemannian product space. Then, when the base $M$ is conformal to a …

Study on special warped product manifolds with Einstein metrics.

Study on Ricci-Bourguignon solitons on specific product spaces.

The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.

The study explores Einstein hypersurfaces in warped product spaces and their properties.

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…

Defines and computes a generalized spectral action for Lorentz warped products.

In this paper most of the classes of G2-structures with Einstein induced metric of negative, null or positive scalar curvature are realized. This is carried out by means of warped G2-structures with fiber an Einstein SU(3) manifold. The torsion forms of any warped G2-structure are explicitly described in terms of the t…

Study Einstein warped-product manifolds with specific curvature conditions.

Einstein metrics on products are shown to be warped.

The paper examines conditions for Einstein multiply warped products and estimates their parameters.

The paper studies Einstein-type structures in warped product manifolds.

In this paper we take the perspective introduced by Case-Shu-Wei of studying warped product Einstein metrics through the equation for the Ricci curvature of the base space. They call this equation on the base the $m$-Quasi Einstein equation, but we will also call it the $(λ,n+m)$-Einstein equation. In this paper we ext…

The paper examines gradient ρ-Einstein solitons on specific manifolds and spacetimes.

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…

Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.

In this paper, we study the Einstein warped products and multiply warped products with a quarter-symmetric connection. We also study warped products and multiply warped products with a quarter-symmetric connection with constant scalar curvature. Then apply our results to generalized Robertson-Walker spacetimes with a q…

A. Gray presented an interesting $O\left( n\right)$ invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what con…

In this paper we show that a compact warped product Einstein manifold with vanishing Bach tensor of dimension $n \geq 4$ is a finite quotient of a warped product with $(n-1)$-dimensional Einstein fiber. The fiber has constant curvature if $n=4$.

We study warped products semi-Riemannian Einstein manifolds. We consider the case in that the base is conformal to an n-dimensional pseudo Euclidean space and invariant under the action of an translation group. We provide all such solutions in the case Ricci flat when the base is conformal to an n-dimensional pseudo-Eu…

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…

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…

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…

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.

In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of spacetimes called as generalized Kasner space-times, we apply our results to this kind of spac…

We characterize Ricci almost solitons on semi-Riemannian warped products, considering the potential function to depend on the fiber or not. We show that the fiber is necessarily an Einstein manifold. As a consequence of our characterization we prove that when the potential function depends on the fiber, if the gradient…

The paper studies Einstein submanifolds in Euclidean space and finds conditions for their properties.

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…

Backward propagation rules for warped products under Ricci flow.

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…

We examine the space of solutions to the affine quasi--Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitions, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descript…