Related papers: Petrov D vacuum spaces revisited: Identities and I…

A classification of Petrov type D Killing spinor space-times admitting a homogeneous conformal representant is presented. For each class a canonical line-element is constructed and a physical interpretation of its conformal members is…

In an effort to invariantly characterize the conformal curvature structure of analogue spacetimes built from a nonrelativistic fluid background, we determine the Petrov type of a variety of laboratory geometries. Starting from the simplest…

We review the theory of alignment in Lorentzian geometry and apply it to the algebraic classification of the Weyl tensor in higher dimensions. This classification reduces to the the well-known Petrov classification of the Weyl tensor in…

We study the geometric properties of holomorphic distributions of totally null $m$-planes on a $(2m+\epsilon)$-dimensional complex Riemannian manifold $(\mathcal{M}, \bm{g})$, where $\epsilon \in {0,1}$ and $m \geq 2$. In particular, given…

We discuss Petrov type D Einstein-Maxwell fields in which both double null eigenvectors of the Weyl tensor are non-aligned with the eigenvectors of a non-null electromagnetic field and are assumed to be geodesic, shear-free, diverging and…

We analyze oriented Riemannian 4-manifolds whose Weyl tensors $W$ satisfy the conformally invariant condition $W(T,\cdot,\cdot,T) = 0$ for some nonzero vector $T$. While this can be algebraically classified via $W$'s normal form, we find a…

Starting with a subclass of the four-dimensional spaces possessing two commuting Killing vectors and a non-trivial Killing tensor, we fully integrate Einstein's vacuum equation with a cosmological constant. Although most of the solutions…

We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars $\Psi_{1}$ and $\Psi_{3}$ equal to zero, assuming that initially all the Weyl scalars are non vanishing.…

Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this induces a map from a generally covariant…

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms…

Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…

We employ the Cartan-Karlhede algorithm in order to completely characterize the class of G\"odel-like spacetimes for three-dimensional gravity. By examining the permitted Segre types (or P-types) for the Ricci tensor we present the results…

We consider a general class of four-dimensional geometries admitting a null vector field that has no twist and no shear but has an arbitrary expansion. We explicitly present the Petrov classification of such Robinson-Trautman (and Kundt)…

We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamical part of the spatial connection is fixed to zero by an adequate guage transformation. This new action…

We compute the integral homology and cohomology groups of configuration spaces of two distinct points on a given real projective space. The explicit answer is related to the (known multiplicative structure in the) integral cohomology---with…

We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de…

We give a classification of irreducible four-dimensional symmetric spaces $G/H$ which admit compact Clifford-Klein forms, where $G$ is the transvection group of $G/H$. For this, we develop a method that applies to particular 1-connected…

This paper is devoted to the equivalence of various characterizations of holomorphic $H^1$ Hardy spaces on tube domains over polyhedral cones. We establish a new iterated Poisson integral formula which reproduces holomorphic functions on…

The images of Hermite and Laguerre Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterised. These are used to characterise the Schwartz class of rapidly decreasing functions. The image of the space…

The integrableTeichm\"uller space $T_p$ for $p \geq 1$ is defined by the $p$-integrability of Beltrami coefficients. We characterize a quasisymmetric homeomorphism $h$ in $T_p$ by the condition that $\log h'$ belongs to the real $p$-Besov…