Related papers: Einstein metrics on aligned homogeneous spaces wit…

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space $G/H$ if…

We study 4-dimensional Poincar\'e-Einstein manifolds whose conformal class contains a K\"ahler metric. Such Einstein metrics are non-K\"ahler and admit a Killing field extending to the conformal infinity, and the Einstein equation reduces…

Let $G$ be a compact connected Lie group and $H$ a closed subgroup of $G$. Suppose the homogeneous space $G/H$ is effective and has dimension 3 or higher. Consider a $G$-invariant, symmetric, positive-semidefinite, nonzero (0,2)-tensor…

We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If $M$ is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein…

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group…

Given a quantum subgroup $G\subset U_n$ and a number $k\leq n$ we can form the homogeneous space $X=G/(G\cap U_k)$, and it follows from the Stone-Weierstrass theorem that $C(X)$ is the algebra generated by the last $n-k$ rows of coordinates…

The spacetime homogeneous G\"odel-type spacetimes which have four classes of metrics are studied according to their matter collineations. The obtained results are compared with Killing vectors and Ricci collineations. It is found that these…

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…

A homogeneous Riemannian space $(M= G/H,g)$ is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group $G$. We study the structure of compact GO-spaces and give some…

The five-dimensional (5D) Riemannian G\"odel-type manifolds are examined in light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are…

On $4$-symmetric symplectic spaces, invariant almost complex structures -- up to sign -- arise in pairs. We exhibit some $4$-symmetric symplectic spaces, with a pair of "natural" compatible (usually not positive) invariant almost complex…

We describe the $10$-dimensional space of $Sp(2)$-invariant $G_2$-structures on the homogeneous $7$-sphere $S^7=Sp(2)/Sp(1)$ as $\mathbb{R}^+\times Gl^+(3,\mathbb{R})$. In those terms, we formulate a general Ansatz for $G_2$-structures,…

Let $M$ be a compact K\"ahler manifold and $N$ be a subvariety with codimension greater than or equal to 2. We show that there are no complete K\"ahler--Einstein metrics on $M-N$. As an application, let $E$ be an exceptional divisor of $M$.…

We consider 4-dimensional spacetime manifolds that are piecewise Lorentzian, where the Lorentzian components of the manifold are separated by codimension-one planes (spacelike or timelike) on which the metric is degenerate. Such manifolds…

We consider homogeneous hypercomplex manifolds with a transitive action of a compact Lie group and we give a characterization of invariant HKT metrics on them. On every such hypercomplex manifold we prove the existence of an invariant…

The third real de Rham cohomology of compact homogeneous spaces is studied. Given $M=G/K$ with $G$ compact semisimple, we first show that each bi-invariant symmetric bilinear form $Q$ on $\mathfrak{g}$ such that…

We consider $(1+ 8)$- and $(1+10)$-dimensional Einstein-Gauss-Bonnet models with the cosmological $\Lambda$-term. Some new examples of exact solutions with three constant Hubble-like parameters in this model are obtained, governed by three…

In this paper we employ numerical methods to study the Einstein equation \[ Ric(g)=\lambda\, g, \] where $Ric$ is the Ricci tensor and $\lambda$ is the Einstein constant, restricted to a class of full flag manifolds. These metrics describe…

Beginning with a special form of the Einstein-Rosen metric, we find new cosmological solutions of the Einstein equations, having two hypersurface-orthogonal Killing vectors , with ideal fluid. The equation of state is in the most cases of…

We study the geometry of Lie groups $G$ with a continuous Finsler metric, assuming the existence of a subgroup $K$ such that the metric is right-invariant for the action of $K$. We present a systematic study of the metric and geodesic…