Thierry Barbot

Globally hyperbolic flat space–times

Abstract We consider (flat) Cauchy-complete GH space–times, i.e., globally hyperbolic flat Lorentzian manifolds admitting some Cauchy hypersurface on which the ambient Lorentzian metric restricts as a complete Riemannian metric. We define a family of such space–times—model space–times—including four subfamilies: translation space–times, Misner space–times, unipotent space–times, and Cauchy-hyperbolic space–times (the last family—undoubtful the most interesting one—is a generalization of standard space–times defined by G. Mess). We prove that, up to finite coverings and (twisted) products by Euclidean linear spaces, any Cauchy-complete GH space–time can be isometrically embedded in a model space–time, or in a twisted product of a Cauchy-hyperbolic space–time by flat Euclidean torus. We obtain as a corollary the classification of maximal GH space–times admitting closed Cauchy hypersurfaces. We also establish the existence of CMC foliations on every model space–time.

Collisions of Particles in Locally AdS Spacetimes I. Local Description and Global Examples

We investigate 3-dimensional globally hyperbolic AdS manifolds (or more generally constant curvature Lorentz manifolds) containing “particles”, i.e., cone singularities along a graph Γ. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than 2π on time-like singular segments). We construct examples of such manifolds, describe the cone singularities that can arise and the way they can interact (the local geometry near the vertices of Γ). We then adapt to this setting some notions like global hyperbolicity which are natural for Lorentz manifolds, and construct some examples of globally hyperbolic AdS manifolds with interacting particles.

A primer on the (2 + 1) Einstein universe

The Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is to develop the synthetic geometry of the Einstein universe in terms of its homogeneous submanifolds and causal structure, with particular emphasis on dimension 2+1, in which there is a rich interplay with symplectic geometry.This is a survey about conformal mappings between pseudo-Riemannian manifolds and, in particular, conformal vector fields defined on such. Mathematics Subject Classification (2000). Primary 53C50; Secondary 53A30; 83C20.We study the geometry of type II supergravity compactifications in terms of an oriented vector bundle

Group Actions on Lorentz Spaces, Mathematical Aspects: A Survey

E

Pseudo-Anosov flows in toroidal manifolds

, endowed with a bundle metric of split signature and further datum. The geometric structure is associated with a so-called generalised

Transitivity of codimension-one Anosov actions of ℝ k on closed manifolds

G

Plane affine geometry and Anosov flows

-structure and characterised by an

Classification and rigidity of totally periodic pseudo-Anosov flows in graph manifolds

E

ALGEBRAIC ANOSOV ACTIONS OF NILPOTENT LIE GROUPS

-spinor

Flag Structures on Seifert Manifolds

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