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Comptes Rendus Mathématique
Volume 342, n° 11
pages 865-868 (juin 2006)
Doi : 10.1016/j.crma.2006.04.009
Received : 19 December 2005 ;  accepted : 1 April 2006
Vector fields dynamics as geodesic motion on Lie groups
Dynamique des champs vectoriels comme mouvement géodésique des groupes de Lie
 

Gabriel Teodor Pripoae
University of Bucharest, Faculty of Mathematics and Informatics, 14 Academiei St., Bucharest, Romania 

Abstract

We study to what extent vector fields on Lie groups may be considered as geodesic fields. For a given left invariant vector field on a Lie group, we prove there exists a Riemannian metric whose geodesics are its trajectories. When we consider left invariant metrics, differences between the Riemannian and the Lorentzian cases appear, coded by properties of the Lie algebra. To cite this article: G.T. Pripoae, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.
Résumé

On étudie les conditions pour que les champs de vecteurs sur les groupes de Lie devienent des champs géodésiques. Pour un champ de vecteurs invariant à gauche, donné sur un groupe de Lie, on prouve quʼil existe une métrique riemannienne dont les géodésiques en sont les trajectoires. Dans le cas des métriques invariantes, on met en évidence certaines differences entre le cas riemannien et celui lorentzien, codées par des propriétés de lʼalgèbre de Lie. Pour citer cet article : G.T. Pripoae, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.


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