Mathematical Research Letters

Volume 22 (2015)

Number 4

Deformations of CR manifolds, parametrizations of automorphisms, and applications

Pages: 1089 – 1127

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n4.a7

Authors

Giuseppe Della Sala (Department of Mathematics, University of Vienna, Austria)

Robert Juhlin (Department of Mathematics, University of Vienna, Austria)

Bernhard Lamel (Department of Mathematics, University of Vienna, Austria)

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 $p \in M$, the equivalence locus $E_p = \{ q \in M : (M,q)$ 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.

2010 Mathematics Subject Classification

32H02, 32V40

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