[Sur la géométrie de lumière : actions isométriques et rigidité]
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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Esmaa Bekkara 1 ; Charles Frances 2 ; Abdelghani Zeghib 3
@article{CRMATH_2006__343_5_317_0,
author = {Esmaa Bekkara and Charles Frances and Abdelghani Zeghib},
title = {On lightlike geometry: isometric actions, and rigidity aspects},
journal = {Comptes Rendus. Math\'ematique},
pages = {317--321},
publisher = {Elsevier},
volume = {343},
number = {5},
year = {2006},
doi = {10.1016/j.crma.2006.07.007},
language = {en},
}
TY - JOUR AU - Esmaa Bekkara AU - Charles Frances AU - Abdelghani Zeghib TI - On lightlike geometry: isometric actions, and rigidity aspects JO - Comptes Rendus. Mathématique PY - 2006 SP - 317 EP - 321 VL - 343 IS - 5 PB - Elsevier DO - 10.1016/j.crma.2006.07.007 LA - en ID - CRMATH_2006__343_5_317_0 ER -
Esmaa Bekkara; Charles Frances; Abdelghani Zeghib. On lightlike geometry: isometric actions, and rigidity aspects. Comptes Rendus. Mathématique, Volume 343 (2006) no. 5, pp. 317-321. doi : 10.1016/j.crma.2006.07.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.07.007/
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