Related papers: Survey: Homogeneous Einstein Manifolds

We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces $\mathrm{SU}(n)$, $n\geq3$, and $E_6/F_4$. Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces…

This article describes some geometric invariants and conformal anomalies for conformally compact Einstein manifolds and their minimal submanifolds which have recently been discovered via the Anti-de Sitter/Conformal Field Theory…

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian…

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…

The Einstein-Klein-Gordon field equations are solved in a inhomogeneous shear-free universe containing a material fluid, a self-interacting scalar field, a variable cosmological term, and a heat flux. A quintessence-dominated scenario…

We provide a classification of Einstein submanifolds in space forms with flat normal bundle and parallel mean curvature. This extends a previous result due to Dajczer and Tojeiro for isometric immersions of Riemannian manifolds with…

In this paper, we present some new properties for p-biharmonic hypersurfaces in Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces.…

This paper produces explicit strongly Hermitian Einstein-Maxwell solutions on the smooth compact $4$-manifolds that are $S^2$-bundles over compact Riemann surfaces of any genus. This generalizes the existence results by C. LeBrun in…

The paper surveys the history and state-of-the-art of the study of Jordan homomorphisms.

M.~M.~Graev associated in \cite{Gr} to a compact homogeneous space $G/H$ a nerve $\XGH$, whose non-contractibility implies the existence of a $G$-invariant Einstein metric on $G/H$. The nerve $\XGH$ is a compact semi-algebraic set, defined…

The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we…

We analyze the relationship between Hausdorffness and homogeneity in the frame of manifolds, not confined to be Hausdorff. We exhibit examples of homogeneous non-Hausdorff manifolds and prove that a Lindel\"of homogeneous manifold is…

In this paper, we classify three-locally-symmetric spaces for a connected, compact and simple Lie group. Furthermore, we give the classification of invariant Einstein metrics on these spaces.

This survey contains the main results in rational homotopy, from the beginning to the most recent ones. It makes the status of the art, gives a short presentation of some areas where rational homotopy has been used, and contains a lot of…

We classify the Einstein metrics on closed 4-manifolds whose isometry group has dimension at least 3. Consequently, we show that the cohomogeneity-one Einstein metrics on a closed $4$-manifold are locally symmetric or homothetic to the Page…

Given a non compact semisimple Lie group $G$ we describe all homogeneous spaces $G/L$ carrying an invariant almost K\"ahler structure $(\omega,J)$. When $L$ is abelian and $G$ is of classical type, we classify all such spaces which are…

This is a collection of notes on the properties of left-invariant metrics on the eight-dimensional compact Lie group SU(3). Among other topics we investigate the existence of invariant pseudo-Riemannian Einstein metrics on this manifold. We…

Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the case that the corresponding Lie algebra…

Let (M,g) be an Einstein manifold of dimension n \geq 4 with nonnegative isotropic curvature. We show that (M,g) is locally symmetric.

A para-K\"ahler manifold can be defined as a pseudo-Riemannian manifold $(M,g)$ with a parallel skew-symmetric para-complex structures $K$, i.e. a parallel field of skew-symmetric endomorphisms with $ K^2 = \mathrm{Id} $ or, equivalently,…