On Lie groups that admit left-invariant Lorentz metrics of constant sectional curvature
type: Item
instance of: scholarly article
title: On Lie groups that admit left-invariant Lorentz metrics of constant sectional curvature
zbMATH Open document ID: 0679.53039
author: Frank Barnet
published in: Illinois Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let G be a Lie group which admits a left-invariant Riemannian metric of constant negative sectional curvature. The main theorem in this paper states that: i) G admits a left-invariant Lorentz metric of constant positive sectional curvature, ii) G admits a left-invariant Lorentz metric of constant negative, or zero, sectional curvature if and only if its Lie algebra contains a one-dimensional ideal. Combining this with a previous result of E. Heintze, the author proves that such even- dimensional groups G admit left-invariant Lorentz metrics with constant sectional curvature of any possible sign, whereas this may be wrong for odd-dimensional groups.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 22E15
zbMATH DE Number: 4113455
zbMATH Keywords: Lie group
zbMATH Keywords: left-invariant Riemannian metric
zbMATH Keywords: left-invariant Lorentz metric
reviewed by: François Rouvière
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4113455