Deformations of CR manifolds, parametrizations of automorphisms, and applications
- Author(s)
- Giuseppe Della Sala, Robert Juhlin, Bernhard Lamel
- Abstract
We prove a parametrization theorem for maps of deformations of minimal, holomorphically nondegenerate real-analytic CR manifolds. This is used to deduce results on biholomorphic equivalence; we show that one can, for any germ of a minimal, holomorphically nondegenerate real-analytic CR manifold (M,p) construct a function which completely characterizes the CR manifolds biholomorphically equivalent to (M,p). As an application, we show that for any p ε M, the equivalence locus Ep = {q ε M : (M,q) biholomorphically equivalent to (M,p)} is a locally closed real-analytic submanifold of M, and give a criterion for the global CR automorphism group to be a (finite-dimensional) Lie group.
- Organisation(s)
- Department of Mathematics
- Journal
- Mathematical Research Letters
- Volume
- 22
- Pages
- 1089-1127
- No. of pages
- 39
- ISSN
- 1073-2780
- DOI
- https://doi.org/10.4310/MRL.2015.v22.n4.a7
- Publication date
- 2015
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis, 101009 Geometry, 101008 Complex analysis
- Keywords
- ASJC Scopus subject areas
- Mathematics(all)
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/deformations-of-cr-manifolds-parametrizations-of-automorphisms-and-applications(4c03122f-2b63-400a-8064-21cc8fd5bcf2).html