On the stability group of CR manifolds Academic Article uri icon


  • 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 = (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 = (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). 2006 Acadmie des sciences.

published proceedings

  • Comptes Rendus Mathmatique

author list (cited authors)

  • Lamel, B., & Mir, N.

citation count

  • 0

complete list of authors

  • Lamel, Bernhard||Mir, Nordine

publication date

  • August 2006