Related papers: Einstein tori and crooked surfaces
It is of interest to characterize algebraically the dynamical types of isometries of the complex and quaternionic hyperbolic planes. In the complex case, such a characterization is known from the work of Giraud-Goldman. In this paper, we…
We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally…
We show that the system of vacuum Einstein equations (i.e., Ricci-flat metrics) with two hypersurface-orthogonal, commuting Killing vector fields in $d \ge 5$ dimensions is invariant under the action of a one-parameter Lie group, and the…
We consider a $D$-dimensional cosmological model with a dilaton field and two $(D-d-1)$-form field strengths which have nonvanishing fluxes in extra dimensions. Exact solutions for the model with a certain set of couplings are obtained by…
We show that, given an arbitrary shift, the lapse $N$ can be chosen so that the extrinsic curvature $K$ of the space slices with metric $\overline g$ in arbitrary coordinates of a solution of Einstein's equations satisfies a quasi-linear…
Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the…
The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts.…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
A map is discussed that connects, in 1+1 dimensions, Galilei's relativity to Einstein's special relativity. By means of this map it is possible to derive special-relativistic formulas from the corresponding Galilean ones. Beyond being…
In this paper we investigate a class of solutions of Einstein equations for the plane-symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the…
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 demonstrate how the Einstein's equations for the $D$-dimensional spherical gravity can be written in the covariant vector-like form. These equations reveal easily the causal structure of curved spherically symmetric manifolds and may…
We prove that the set of non-degenerate second order maximally superintegrable systems in the complex Euclidean plane carries a natural structure of a projective variety, equipped with a linear isometry group action. This is done by…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
We present a covariant decomposition of Einstein's Field Equations which is particularly suitable for perturbations of spherically symmetric -- and general locally rotationally symmetric -- spacetimes. Based upon the utility of the 1+3…
We prove in the cases of plane and hyperbolic symmetries a global in time existence result in the future for comological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a distribution function and a…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
We describe and study the loci equidistant from finitely many points in the so-called complex hyperbolic geometry, i.e., in the geometry of a holomorphic $2$-ball $\Bbb B$. In particular, we show that the bisectors (= the loci equidistant…
In this paper we study fundamental properties of geodesic mappings with respect to the smoothness class of metrics. We show that geodesic mappings preserve the smoothness class of metrics. We study geodesic mappings of Einstein spaces.
We describe a method to obtain $\mathrm{SU}(3)$-structures and $\mathrm{G}_2$-structures on 6 and 7-dimensional manifolds respectively, such that its associated metric is Einstein. More concretely, we have that different classes of…