CR structures of codimension 2
type: Item
instance of: scholarly article
title: CR structures of codimension 2
zbMATH Open document ID: 0675.32017
author: Robert I. Mizner
published in: Journal of Differential Geometry
publication date: 1989-01-01T00:00:00Z
review text: Let M be a smooth \((2n+k)\)-dimensional manifold. A CR structure of dimension n and codimension k is a pair (D,J), where \(D\subset TM\) is a smooth subbundle of fibre dimension 2n and J is a bundle automorphism of D satisfying: \(J^ 2=-1\) and \(J([X,Y]-[JX,JY])=[JX,Y]+[X,JY]\) for sections X and Y of D. There are several methods of associating a Cartan connection on a principal bundle to a nondegenerate codimension 1 CR structure. In this paper, the author defines a class of admissible codimension 2 CR structures which is an analogous to the class of nondegenerate CR structures, and for given admissible CR structure on a manifold M he constructs a principal bundle (a subbundle of the frame bundle of M) and a connection on this bundle. Furthermore, he decomposes TM as a direct sum of subbundles of fibre dimensions 1 and 2.
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32G07
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 55R10
zbMATH DE Number: 4105345
zbMATH Keywords: moduli spaces
zbMATH Keywords: CR structure
zbMATH Keywords: nondegenerate CR structures
zbMATH Keywords: admissible CR structure
Wikidata QID: Q115182624
reviewed by: Andrew Bucki
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214443289
OpenAlex ID: W1565928405
DOI: 10.4310/JDG/1214443289
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description: scientific article; zbMATH DE number 4105345