Cohomogeneity one de Sitter space \(S^n_1\)
type: Item
instance of: scholarly article
title: Cohomogeneity one de Sitter space \(S^n_1\)
zbMATH Open document ID: 1207.53070
author: Sumit K. Garg
publication date: 2010-10-29T00:00:00Z
review text: The paper belongs to the literature on non-transitive actions of the isometry groups of (pseudo-) Riemannian manifolds. A distinguished topic deals with ``cohomogeneity one'' (pseudo-) Riemannian manifolds, defined by an action with an orbit of codimension one and no orbit of codimension zero. Indeed, several results have been achieved in the literature for the Riemannian case. But, in the pseudo-Riemannian case, a difficulty arises from the fact that the action of closed Lie subgroups of the group of isometries does not need to be proper. In the present paper, the authors contribute to overcoming this difficulty. They study the distinguished case of a de Sitter space. Indeed, they study the actions in both proper and non-proper cases. In the first case, they characterise the acting groups and orbits and prove that the orbit space is homeomorphic to \(\mathbb R\). In the second case, they determine the groups and the orbits in some different cases and prove that the orbit space is not Hausdorff.
reviewed by: Marco Modugno
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 5808622
zbMATH Keywords: cohomogeneity one
zbMATH Keywords: Lorentzian space
zbMATH Keywords: de Sitter space
MaRDI profile type: Publication
full work available at URL: s10114-010-8142-3
OpenAlex ID: W1986591360
cites work: Q4370979
cites work: Some topological properties of cohomogeneity one manifolds with negative curvature
cites work: A General Theory of Canonical Forms
cites work: Cohomogeneity and positive curvature in low dimensions
cites work: Invariant metrics on cohomogeneity one manifolds
cites work: Cohomogeneity one Minkowski space Rn1
cites work: The geometry of homogeneous submanifolds of hyperbolic space
cites work: Lie groups
cites work: Q5658847
cites work: Lie groups and Lie algebras III. Structure of Lie groups and Lie algebras. Transl. from the Russian by V. Minachin
cites work: Q4516132
cites work: Cohomogeneity one Riemannian manifolds of non-positive curvature
cites work: Some remarks about Lie groups transitive on spheres and tori
cites work: Q3741813
cites work: Q5546515
cites work: Q4819371
cites work: Maximal Abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces
DOI: 10.1007/S10114-010-8142-3
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5808622