Related papers: Weakly Einstein conformal products

Let $(M^n,g)$, $n \ge 4$, be a compact simply-connected Riemannian manifold with nonnegative isotropic curvature. Given $0<l\le L$, we prove that there exists $\eps = \eps (l,L,n)$ satisfying the following: If the scalar curvature $s$ of…

We show that under some natural geometric assumption, Einstein metrics on conformal products of two compact conformal manifolds are warped product metrics.

We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kahler-Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat…

The goal of this paper is to study weakly Einstein critical metrics of the volume functional on a compact manifold $M$ with smooth boundary $\partial M$. Here, we will give the complete classification for an $n$-dimensional, $n=3$ or $4,$…

An almost Einstein manifold satisfies equations which are a slight weakening of the Einstein equations; Einstein metrics, Poincare-Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are…

This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous…

A method, due to \'Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant…

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…

If $M$ is the underlying smooth oriented $4$-manifold of a Del Pezzo surface, we consider the set of Riemannian metrics $h$ on $M$ such that $W^+(\omega , \omega )> 0$, where $W^+$ is the self-dual Weyl curvature of $h$, and $\omega$ is a…

Inspired by the problem of classifying Einstein manifolds with positive scalar curvature, we prove that an Einstein four-manifold whose associated twistor space has scalar curvature constant on the fibers of the twistor bundle is half…

We classify weakly Einstein submanifolds in space forms that satisfy Chen's equality. We also give a classification of weakly Einstein hypersurfaces in space forms that satisfy the semisymmetric condition. In addition, we discuss some…

For warped products with harmonic curvature, nonconstant warping functions $\phi$, and compact two-dimensional bases $(M,h)$, we establish a dichotomy: either the Gaussian curvature $K$ of the metric $g=\phi^{-2}h$ is constant and negative,…

Let $R$ be a constant. Let $\mathcal{M}^R_\gamma$ be the space of smooth metrics $g$ on a given compact manifold $\Omega^n$ ($n\ge 3$) with smooth boundary $\Sigma $ such that $g$ has constant scalar curvature $R$ and $g|_{\Sigma}$ is 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…

This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational…

We prove the instability of conformally K\"ahler, compact or ALF Einstein 4-manifolds with nonnegative scalar curvature which are not half conformally flat. This applies to all the known examples of gravitational instantons which are not…

We construct new homogeneous Einstein spaces with negative Ricci curvature in two ways: First, we give a method for classifying and constructing a class of rank one Einstein solvmanifolds whose derived algebras are two-step nilpotent. As an…

We prove the following statement: Let g be a light-line-complete pseudo-Riemannian Einstein metric of indefinite signature on a connected (n>2)-dimensional manifold M. Assume that a conformally equivalent metric is also Einstein. Then, the…

We derive the general formulas for a special configuration of the sequential warped product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a conformal metrics.…

A Riemannian metric $\wht{g}$ with Ricci curvature $\wht{\ri}$ is called nontrivial quasi-Einstein, in the sense of Case, Shu and Wei, if it satisfies $(-a/f)\wht{\nab} df+\wht{\ri}=\lambda \wht{g}$, for a smooth nonconstant function $f$…