Lie group structures on automorphisms groups of real-analytic CR manifolds

Bernhard Lamel (1) , Nordine Mir (2) , Dmitri Zaitsev (3)

1 Fakultät für Mathematik [Wien]
2 LMRS - Laboratoire de Mathématiques Raphaël Salem
3 TCD - School of Mathematics

Given any real-analytic CR manifold $M$, we provide general conditions on $M$ guaranteeing that the group of all its global real-analytic CR automorphisms $\Aut_\CR(M)$ is a Lie group (in an appropriate topology). In particular, we obtain a Lie group structure for $\Aut_\CR(M)$ when $M$ is an arbitrary compact real-analytic hypersurface embedded in some Stein manifold.

Mots clés: Global CR automorphism group; Lie group structure; jet parametrization

Domaines: Variables complexes [math.CV]; Géométrie différentielle [math.DG]

Bernhard Lamel, Nordine Mir, Dmitri Zaitsev. Lie group structures on automorphisms groups of real-analytic CR manifolds. American Journal of Mathematics, 2008, 130 (6), pp.1709--1726. ⟨hal-00261705⟩