Automorphism groups of minimal real-analytic CR manifolds
A connected real-analytic embedded CR manifold \(M\) is called holomorphically non-degenerate if at any of its points there is no nontrivial germ of a holomorphic vector field tangent to \(M\). For a minimal CR-manifold \(M\) this condition is known to be sufficient and necessary for the Lie algebra of infinitesimal automorphisms to be finite dimensional (see [\textit{M. S. Baouendi, P. Ebenfelt} and \textit{L. P. Rothschild}, Commun. Anal. Geom. 6, No. 2, 291--315 (1998; Zbl 0982.32030)]). In the paper under review the authors construct a jet parametrisation for such CR manifolds. As a consequence they prove that for a connected real-analytic CR-manifold that is minimal at a point \(p\) the group \(\text{Aut}(M,p)\) of local real-analytic CR-automorphisms at \(p\) is a finite-dimensional Lie group if and only if \(M\) is holomorphically non-degenerate. In this case the group \(\text{Aut}(M,p)\) can be identified with a real algebraic subgroup of a finite order jet-group.
scientific article; zbMATH DE number 6142947
scientific article