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CR Mappings of Circular CR Manifolds

Published online by Cambridge University Press:  20 November 2018

André Boivin  and
Roman Dwilewicz
André Boivin
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, N6A 5B7, e-mail:boivin@uwovax.uwo.cardwilewi@uwovax.uwo.ca
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Abstract

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Let M be a circular CR manifold and let N be a rigid CR manifold in some complex vector spaces. The problem of the existence of local CR mappings from M into N is considered. Conditions are given which ensure that the space of such CR mappings depends on a finite number of parameters. The idea of the proof of the main result relies on a Bishop type equation for CR mappings. Roughly speaking, we look for CR mappings from M into N in the form F = (ƒ,g), we assume that g is given, then we find ƒ in terms of g and some parameters, and finally we look for conditions on g. It works independently of assumptions on the Levi forms of M and N, and there is also some freedom on the codimension of the manifolds.

Keywords

32C1632H9958C10CR mappingsCR manifolds
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 4 , 01 December 1995 , pp. 396 - 407
Copyright
Copyright © Canadian Mathematical Society 1995

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