Related papers: Simple Space-Time Symmetries: Generalizing Conform…

Given a smooth free action of a compact connected Lie group $G$ on a smooth compact manifold $M$, we show that the space of $G$-invariant Riemannian metrics on $M$ whose automorphism group is precisely $G$ is open dense in the space of all…

Among all plastic deformations of the gravitational Lorentz vacuum \cite{wr1} a particular role is being played by conformal deformations. These are conveniently described by using the homogeneous space for the conformal group…

Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of…

Classical noncompact reductive Lie group $G$ admits a compactification $\overline{G}$ as a Riemannian symmetric space by He. First, we provide a unified construction of these compactifications via Grassmannian geometry and realize the group…

For a Lie group G, we seek the right definition of a "moment space" for G. One axiom is clear, involving a closed equivariant three-form. We construct this form for symmetric spaces associated to a symmetric pair (H,G) with an additional…

Let us call a (para)topological group \emph{strongly submetrizable} if it admits a coarser separable metrizable (para)topological group topology. We present a characterization of simply $sm$-factorizable (para)topo\-logical groups by means…

We solve the Killing spinor equations of supersymmetric IIB backgrounds which admit one supersymmetry and the Killing spinor has stability subgroup G_2 in Spin(9,1) x U(1). We find that such backgrounds admit a time-like Killing vector…

We propose a superspace formulation for conformal $(p,q)$ supergravity in two dimensions as a gauge theory of the superconformal group $\mathsf{OSp}_0 (p|2; {\mathbb R} ) \times \mathsf{OSp}_0 (q|2; {\mathbb R} )$ with a flat connection.…

Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques do not directly apply. We show that, when a group $G$ acts…

Riemannian geodesic orbit spaces (G/H,g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S,g), where…

A classification is given of the exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional compact Lie group or $S\!pin(8)$, and moreover the structure of $K$ is determined as Lie…

Minkowski space, conformal group, compactification, conformal infinity, conformal inversion, light cone at infinity, SU(2,2), SO(4,2), Hodge star operator, Clifford algebra, spinors, twistors, antilinear operators, exterior algebra,…

We classify contact manifolds $(M,\mathcal D)$ which are homogeneous under a connected semisimple Lie group $G$, and symmetric in the sense that there exists a contactomorphism of $(M,\mathcal D)$ normalizing $G$, fixing a point $o$ in $M$…

Let $G$ be a real linear algebraic group and $L$ a finitely generated cosimplicial group. We prove that the space of homomorphisms $Hom(L_n,G)$ has a homotopy stable decomposition for each $n\geq 1$. When $G$ is a compact Lie group, we show…

Let $X$ be a compact connected Riemann surface, $D\, \subset\, X$ a reduced effective divisor, $G$ a connected complex reductive affine algebraic group and $H_x\, \subsetneq\, G_x$ a Zariski closed subgroup for every $x\, \in\, D$. A framed…

Let M denote either Euclidean or hyperbolic n-space, and let G be a discrete group of isometries of M, with the property that G respects and acts tile-transitively on a convex-polyhedral tesselation of M. Given an arbitrary base point p in…

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…

Globally hyperbolic spacetimes with timelike boundary $(\overline{M} = M \cup \partial M, g)$ are the natural class of spacetimes where regular boundary conditions (eventually asymptotic, if $\overline{M}$ is obtained by means of a…

We generalize the notion of kinematical Lie algebra introduced in physics for the classification of the various possible relativity algebras an isotropic spacetime can accommodate. We first give an elementary proof of the fact that such a…

Nurowski showed that any generic 2-plane field $D$ on a 5-manifold $M$ determines a natural conformal structure $c_D$ on $M$; these conformal structures are exactly those (on oriented $M$) whose normal conformal holonomy is contained in the…