On the stability group of CR manifolds

Bernhard Lamel, Nordine Mir

Research output: Contribution to journalArticle

Abstract

For any essentially finite minimal real-analytic generic submanifold M ⊂ CN, N ≥ 2, we show that for every point p ∈ M the local real-analytic CR automorphisms of M fixing p can be parametrized real-analytically by their ℓ = ℓ (p) jets at p. As an application, we derive a Lie group structure for the stability group Aut (M, p). We also show that the order ℓ = ℓ (p) of the jet space in which the group Aut (M, p) embeds can be chosen to depend upper-semicontinuously on p. This yields that given any compact real-analytic minimal CR submanifold M in CN, there exists an integer k depending only on M such that for every point p ∈ M local CR diffeomorphisms mapping a neighbourhood of p in M into another real-analytic CR submanifold in CN with the same CR dimension as that of M are uniquely determined by their k-jet at p. To cite this article: B. Lamel, N. Mir, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

Original languageEnglish
Pages (from-to)169-172
Number of pages4
JournalComptes Rendus Mathematique
Volume343
Issue number3
DOIs
Publication statusPublished - 1 Aug 2006
Externally publishedYes

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CR Manifold
CR-submanifold
Jet Space
Diffeomorphisms
Submanifolds
Automorphisms
Integer

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the stability group of CR manifolds. / Lamel, Bernhard; Mir, Nordine.

In: Comptes Rendus Mathematique, Vol. 343, No. 3, 01.08.2006, p. 169-172.

Research output: Contribution to journalArticle

Lamel, Bernhard ; Mir, Nordine. / On the stability group of CR manifolds. In: Comptes Rendus Mathematique. 2006 ; Vol. 343, No. 3. pp. 169-172.
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