### Abstract

For any essentially finite minimal real-analytic generic submanifold M ⊂ C^{N}, 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 C^{N}, 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 C^{N} 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 language | English |
---|---|

Pages (from-to) | 169-172 |

Number of pages | 4 |

Journal | Comptes Rendus Mathematique |

Volume | 343 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Aug 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Comptes Rendus Mathematique*,

*343*(3), 169-172. https://doi.org/10.1016/j.crma.2006.06.016

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

Research output: Contribution to journal › Article

*Comptes Rendus Mathematique*, vol. 343, no. 3, pp. 169-172. https://doi.org/10.1016/j.crma.2006.06.016

}

TY - JOUR

T1 - On the stability group of CR manifolds

AU - Lamel, Bernhard

AU - Mir, Nordine

PY - 2006/8/1

Y1 - 2006/8/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=33746117329&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746117329&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2006.06.016

DO - 10.1016/j.crma.2006.06.016

M3 - Article

AN - SCOPUS:33746117329

VL - 343

SP - 169

EP - 172

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 3

ER -