Flat pseudo-Riemannian Lie groups
type: Item
instance of: scholarly article
title: Flat pseudo-Riemannian Lie groups
zbMATH Open document ID: 1058.53055
author: A. Medina
author: Anne-Marie Aubert
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2004-08-16T00:00:00Z
review text: A result of \textit{J. W. Milnor} [Adv. Math. 21, 293--329 (1976; Zbl 0341.53030)] describes the structure of Lie groups which carry a flat left-invariant Riemannian metric. The authors are interested in the generalization of this study to the pseudo-Riemannian situation. In the non-definite case, the group is not necessarily complete with respect to the metric, a fact which turns out to be equivalent to the group being unimodular. The authors give methods to construct examples, showing in particular that the skew-cotangent group of an affine group always carries a flat invariant metric with signature \((n,n)\). They finally show that some groups, like the general linear group or the Heisenberg groups of dimension \(\geq 5\) cannot carry such a metric.
reviewed by: Jean-François Quint
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 22E60
zbMATH DE Number: 2091872
zbMATH Keywords: affine Lie groups
zbMATH Keywords: homogeneous geometric stuctures
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113247126
OpenAlex ID: W2047864437
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DOI: 10.2748/TMJ/1113247126
description: scientific article; zbMATH DE number 2091872