Proper Almost-Homogeneous Domains of the Einstein Universe

2024/07/26 by Chalumeau, Adam, Galiay, Blandine · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2407.18577

Abstract

The Einstein universe Ein^p,q of signature (p,q) is a pseudo-Riemannian analogue of the conformal sphere; it is the conformal compactification of the pseudo-Riemannian Minkowski space. For p,q ≥ 1, we show that, up to a conformal transformation, there is only one almost-homogeneous domain in Ein^p,q that is bounded in a suitable stereographic projection. This domain, which we call a diamond, is a model for the symmetric space of PO(p,1) × PO(1,q). We deduce a classification of closed conformally flat manifolds with proper development.

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