Automorphism groups of minimal real-analytic CR manifolds
type: Item
instance of: scholarly article
title: Automorphism groups of minimal real-analytic CR manifolds
zbMATH Open document ID: 1267.32013
DOI: 10.4171/JEMS/366
author: Robert Juhlin
author: Bernhard Lamel
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2013-03-07T00:00:00Z
review text: 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.
reviewed by: Gerd Schmalz
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 6142947
zbMATH Keywords: automorphisms of CR manifolds
zbMATH Keywords: holomorphic nondegeneracy
zbMATH Keywords: minimal CR manifold
MaRDI profile type: Publication
cites work: Algebraicity of holomorphic mappings between real algebraic sets in \(\mathbb{C}^ n\)
cites work: Parametrization of local biholomorphisms of real analytic hypersurfaces
cites work: CR automorphisms of real analytic manifolds in complex space
cites work: Q4230686
cites work: Reflection ideals and mappings between generic submanifolds in complex space
cites work: Q4334541
cites work: Sur la géométrie pseudo-conforme des hypersurfaces de l'espace de deux variables complexes
cites work: Real hypersurfaces in complex manifolds
cites work: When \(\varphi(f)\) convergent implies \(f\) is convergent
cites work: Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case
cites work: FORMAL RELATIONS BETWEEN ANALYTIC FUNCTIONS
cites work: Determination of formal CR mappings by a finite jet
cites work: The Catlin Multitype and Biholomorphic Equivalence of Models
cites work: Normal forms for hypersurfaces of finite type in \(\mathbb C^2\)
cites work: Parametrization of local CR automorphisms by finite jets and applications
cites work: Infinitesimal CR Automorphisms of Rigid Hypersurfaces
cites work: On the pseudo-conformal geometry of hypersurface of the space of \(n\) complex variables
cites work: Germs of local automorphisms of real-analytic CR structures and analytic dependence on \(k\)-jets
full work available at URL: https://doi.org/10.4171/jems/366
OpenAlex ID: W1973781675
description: scientific article; zbMATH DE number 6142947