Cohomogeneity one anti de Sitter space \(H^3_1\)
type: Item
instance of: scholarly article
title: Cohomogeneity one anti de Sitter space \(H^3_1\)
zbMATH Open document ID: 1181.53056
author: N. E. Zubov
published in: Bulletin of the Iranian Mathematical Society
publication date: 2009-09-16T00:00:00Z
review text: In this paper the authors study the manifold \(H^3_1\) under the action of a closed Lie subgroup of isometries \(G \subseteq Iso(H^3_1)\) with an orbit of dimension two. It is proved that if \(H_1^3\) is of cohomogeneity one under the proper action of a connected closed Lie group \(G\) of isometries then there exists no space like orbit. The authors determine the acting groups up to conjugacy, \(G\subset SL(2, \mathbb R)\times SL(2,\mathbb R)\). They find the orbits up to isometry and finally they characterize the space \(H^3_1/G\). The results are exposed in several theorems which consider either the existence of a degenerate orbit or the non existence of a degenerate nor a singular orbit.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 5604228
zbMATH Keywords: cohomogeneity one
zbMATH Keywords: anti de Sitter space
reviewed by: Gabriela Paola Ovando
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5604228