Transversal Lie group actions on abstract CR manifolds
type: Item
instance of: scholarly article
title: Transversal Lie group actions on abstract CR manifolds
zbMATH Open document ID: 0673.32021
DOI: 10.1007/BF01446875
author: Linda Preiss Rothschild
author: Mohamed Salah Baouendi
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164667
review text: It is shown that if an abstract CR manifold M has a local transversal Lie group action, then M is locally embeddable as a generic submanifold of \({\mathbb{C}}^ n\). Under the additional assumption that the infinitesimal action of the group forms a subbundle of TM, it is also shown that the action has a local holomorphic extension to \({\mathbb{C}}^ n\) in this embedding. Furthermore, it is shown that there is a unique embedding with this property, up to biholomorphism. Finally, if the action is strictly transversal to the CR structure, it is proved that any CR function can be locally decomposed as a finite sum of boundary values of holomorphic functions in open wedges with edge M.
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 57S20
Mathematics Subject Classification ID: 57S15
zbMATH DE Number: 4101589
zbMATH Keywords: abstract CR manifold
zbMATH Keywords: local transversal Lie group action
zbMATH Keywords: generic submanifold of \({\mathbb{C}}(\sup \) n)
zbMATH Keywords: local holomorphic extension
Wikidata QID: Q115393515
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4101589