On the local equivalence of homogeneous CR-manifolds
type: Item
instance of: scholarly article
title: On the local equivalence of homogeneous CR-manifolds
zbMATH Open document ID: 1092.32021
author: Wilhelm Kaup
published in: Archiv der Mathematik
publication date: 2005-04-28T00:00:00Z
review text: Let us denote by \(\mathcal A\) the class of all CR manifolds \(M\) satisfying the following three conditions: a) \(M\) is compact and simply connected; b) it is locally homogeneous; c) there exists at least one point \(x \in M\) such that the Lie algebra of germs at \(x\) of the infinitesimal CR transformations of \(M\) is finite dimensional. In this paper, the author shows that if \(M, M' \in \mathcal A\), then any local CR equivalence \(f: U \subset M \to U' \subset M'\) extends to a unique global CR equivalence \(f: M \to M'\). The following application is given. In [Invent. Math. 153, No. 1, 45--104 (2003; Zbl 1027.32032)], the author and \textit{D. Zaitsev} considered a special class of homogeneous CR manifolds, which are all realized as compact orbits in a complex vector space of linear actions of certain semisimple Lie groups. In that paper, the classification of those orbits up to global CR equivalence was given. With the result of this paper, the author can prove that the previous classification gives also the classification up to local CR equivalence of the orbits which are simply connected and of those which are non-simply connected but belong to a certain special subclass.
Mathematics Subject Classification ID: 32V20
Mathematics Subject Classification ID: 22F30
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 2162318
zbMATH Keywords: Locally homogeneous CR manifolds
reviewed by: Andrea Spiro
MaRDI profile type: Publication
full work available at URL: s00013-004-1108-x
OpenAlex ID: W1990521003
DOI: 10.1007/S00013-004-1108-X
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description: scientific article; zbMATH DE number 2162318