Harmonicity properties of invariant vector fields on three-dimensional Lorentzian Lie groups
type: Item
instance of: scholarly article
title: Harmonicity properties of invariant vector fields on three-dimensional Lorentzian Lie groups
zbMATH Open document ID: 1221.53093
published in: Journal of Geometry and Physics
publication date: 2011-03-09T00:00:00Z
review text: Let \(G\) be a three-dimensional, simply connected Lie group with a left-invariant Lorentzian metric; \(TG\) is endowed with the Sasaki metric. This paper investigates whether left-invariant vector fields, as maps from \(G\) to \(TG\), define harmonic mappings. Considering in turn each of the possible Lie algebras in this framework, the author studies left-invariant critical points of the ``energy'' \(E\), and of \(E\) restricted to vector fields, or to vector fields of the same constant length for instance.
reviewed by: Satyanad Kichenassamy
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 5862871
zbMATH Keywords: Lie groups with Lorentzian metric
zbMATH Keywords: harmonic maps
zbMATH Keywords: Sasaki metric
Wikidata QID: Q115353289
author: Giovanni Calvaruso
MaRDI profile type: Publication
full work available at URL: j.geomphys.2010.11.001
OpenAlex ID: W1989451080
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DOI: 10.1016/J.GEOMPHYS.2010.11.001
description: scientific article; zbMATH DE number 5862871