Discrete subgroups of complex hyperbolic motions
type: Item
instance of: scholarly article
title: Discrete subgroups of complex hyperbolic motions
zbMATH Open document ID: 0901.32018
author: Ara Basmajian
author: Robert R. Miner
published in: Inventiones Mathematicae
publication date: 1998-11-26T00:00:00Z
review text: The two-dimensional complex hyperbolic space \(CH^2\) is taken as the subset of the projective space \(CP^2\) defined by \(\langle z,z\rangle<0\), where \(\langle , \rangle\) is an indefinite Hermitean product. The paper derives necessary conditions on two elements of the holomorphic isometry group \(PU(2,1)\) to generate a discrete subgroup. Moreover, the authors relate the Carnot-Carathéodory distance and the Cygan distance on the boundary of \(CH^2\) by some explicit formula. They derive a compactness theorem, called the stable basin theorem, for elements close to the identity in \(PU(2,1)\), and they supply conditions for determining when two elements of \(PU(2,1)\) commute in terms of their action on the boundary.
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 30F40
zbMATH DE Number: 1146050
zbMATH Keywords: projective unitary group
zbMATH Keywords: discrete isometry group
zbMATH Keywords: complex hyperbolic space
reviewed by: Rainer Schimming
MaRDI profile type: Publication
full work available at URL: s002220050198
OpenAlex ID: W2081487695
DOI: 10.1007/S002220050198
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description: scientific article; zbMATH DE number 1146050