Differential Geometry/Dynamical Systems
On lightlike geometry: isometric actions, and rigidity aspects
[Sur la géométrie de lumière : actions isométriques et rigidité]
Comptes Rendus. Mathématique, Tome 343 (2006) no. 5, pp. 317-321.

Les métriques riemanniennes dégénérées apparaissent naturellement dans divers contextes. Malheureusement leur étude est souvent limitée par le triste constat qu'elles sont trop pauvres pour donner lieu aux outils classiques de géométrie différentielle, extrinsèque ou intrinsèque, comme par exemple un analogue de la connexion de Levi-Civita. Dans ce papier, nous abordons quelques aspects de la rigidité de ces structures, du point de vue des actions isométriques des groupes de Lie semi-simples.

Degenerate Riemannian metrics exist naturally in various contexts. Unfortunately, their study stops to the ‘admission of failure’ that they are too poor, for instance, to generate a coherent intrinsic or extrinsic differential geometry, e.g. a kind of Levi-Civita connection. In this first text, we start the investigation of rigidity aspects of these structures, from the point of view of isometric actions of ‘big’ (e.g. semi-simple) Lie groups.

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Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.07.007
Bekkara, Esmaa 1 ; Frances, Charles 2 ; Zeghib, Abdelghani 3

1 ENSET-Oran, BP 1523, EL-M'naouer, Oran 31000, Algeria
2 Laboratoire de mathématiques, université Paris sud, 91405 Orsay cedex, France
3 CNRS, UMPA, ENS-Lyon, 46, allée d'Italie, 69364 Lyon cedex 07, France
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Bekkara, Esmaa; Frances, Charles; Zeghib, Abdelghani. On lightlike geometry: isometric actions, and rigidity aspects. Comptes Rendus. Mathématique, Tome 343 (2006) no. 5, pp. 317-321. doi : 10.1016/j.crma.2006.07.007. http://www.numdam.org/articles/10.1016/j.crma.2006.07.007/

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