Lie group structures on groups of diffeomorphisms and applications to CR manifolds

Baouendi, M. Salah; Rothschild, Linda Preiss; Winkelmann, Jörg; Zaitsev, Dimitri

doi:10.5802/aif.2050

Lie group structures on groups of diffeomorphisms and applications to CR manifolds
[Sous-groupes de difféomorphismes, leur structure de groupe de Lie, et applications aux variétés CR]

Baouendi, M. Salah ¹ ; Rothschild, Linda Preiss ; Winkelmann, Jörg ; Zaitsev, Dimitri

¹ University of California, Department of Mathematics, 0112, San Diego, La Jolla, CA 92093-0112 (USA), Université Henri Poincaré Nancy 1, Institut Élie Cartan, B.P. 239, 54506 Vand{\oe}uvre-lès-Nancy Cedex (France), Trinity College, School of Mathematics, Dublin 2 (Irland)

Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1279-1303.

Résumé
Abstract

Nous donnons des conditions suffisantes pour qu'un sous-groupe donné du groupe des difféomorphismes d'une variété indéfiniment differentiable ou réelle analytique ait une structure compatible de groupe de Lie. En utilisant ces résultats, ainsi que des travaux récents concernant la paramétrisation des automorphismes CR par leur jets en un point et leur systèmes complets, nous donnons des conditions sous lesquelles le groupe des automorphismes CR globaux d'une variété CR est un groupe de Lie relativement à une topologie appropriée.

We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.

MR Zbl

DOI : 10.5802/aif.2050

Classification : 22E15, 22F50, 32V20, 32V40, 57S25, 58D05

Affiliations des auteurs :

Baouendi, M. Salah ¹ ; Rothschild, Linda Preiss ; Winkelmann, Jörg ; Zaitsev, Dimitri

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     author = {Baouendi, M. Salah and Rothschild, Linda Preiss  and Winkelmann, J\"org and Zaitsev, Dimitri},
     title = {Lie group structures on groups of diffeomorphisms and applications to {CR} manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {1279--1303},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {5},
     year = {2004},
     doi = {10.5802/aif.2050},
     mrnumber = {2127849},
     zbl = {1062.22046},
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     url = {http://www.numdam.org/articles/10.5802/aif.2050/}
}

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Baouendi, M. Salah; Rothschild, Linda Preiss ; Winkelmann, Jörg; Zaitsev, Dimitri. Lie group structures on groups of diffeomorphisms and applications to CR manifolds. Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1279-1303. doi : 10.5802/aif.2050. http://www.numdam.org/articles/10.5802/aif.2050/

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