Deformations of CR manifolds, parametrizations of automorphisms, and applications

Giuseppe Della Sala; Robert Juhlin; Bernhard Lamel

doi:10.4310/MRL.2015.v22.n4.a7

Deformations of CR manifolds, parametrizations of automorphisms, and applications

Giuseppe Della Sala, Robert Juhlin, Bernhard Lamel

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

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.

Original language	English
Pages (from-to)	1089-1127
Number of pages	39
Journal	Mathematical Research Letters
Volume	22
Issue number	4
DOIs	https://doi.org/10.4310/MRL.2015.v22.n4.a7
Publication status	Published - 2015

Funding

The authors have been supported by the Austrian Federal Ministry of Science and Research through START Prize Y377 and the Austrian Science Fund FWF, project I382. The authors are indebted to Joe Perez for helpful discussions and his invaluable help in designing the software going into the computations presented in Section 7.

Austrian Fields of Science 2012

101002 Analysis
101009 Geometry
101008 Complex analysis

Keywords

SETS

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10.4310/MRL.2015.v22.n4.a7

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AU - Della Sala, Giuseppe

AU - Juhlin, Robert

AU - Lamel, Bernhard

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

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DO - 10.4310/MRL.2015.v22.n4.a7

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JO - Mathematical Research Letters

JF - Mathematical Research Letters

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Deformations of CR manifolds, parametrizations of automorphisms, and applications

Abstract

Funding

Austrian Fields of Science 2012

Keywords

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