On the stability group of CR manifolds - Texas A&M University (TAMU) Scholar

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). © 2006 Académie des sciences.

On the stability group of CR manifolds Academic Article