Crooked surfaces and anti-de Sitter geometry
type: Item
instance of: scholarly article
title: Crooked surfaces and anti-de Sitter geometry
zbMATH Open document ID: 1350.57001
published in: Geometriae Dedicata
publication date: 2015-04-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1302.4911
review text: Crooked planes were defined to bound fundamental polyhedra in Minkowski space for Margulis spacetimes. They where extended to closed polyhedral surfaces, called crooked surfaces, in the conformal compactification of Minkowski space (Einstein space). The conformal model of anti-de Sitter space is the interior of the quotient of Einstein space by an involution fixing an Einstein plane. Crooked surfaces have been defined in the 3-dim anti-de Sitter space \(AdS^3\), and have been used to construct fundamental domains for discrete groups of isometries of \(AdS^3\). (Note that not any complete anti-de Sitter 3-manifold admits a fundamental domain bounded by crooked planes, in contrast with the case of Margulis spacetimes.) The purpose of this work is to interpret \(AdS\)-crooked planes in terms of crooked surfaces in Einstein space. Last but not least, the paper contains a very nice, detailed and useful description of the anti-de Sitter geometry.
reviewed by: Stefano Francaviglia
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 6424926
zbMATH Keywords: Lorentzian geometry
zbMATH Keywords: Minkowski space
zbMATH Keywords: anti-de Sitter space
zbMATH Keywords: symmetric space
zbMATH Keywords: crooked planes
zbMATH Keywords: exponential map
author: William M. Goldman
MaRDI profile type: Publication
OpenAlex ID: W2082822389
arXiv ID: 1302.4911
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DOI: 10.1007/S10711-014-0034-8
description: scientific article