Cartan connections for CR manifolds
type: Item
instance of: scholarly article
title: Cartan connections for CR manifolds
zbMATH Open document ID: 1145.32018
author: Anbo Le
published in: Manuscripta Mathematica
publication date: 2007-09-11T00:00:00Z
review text: For a strictly pseudoconvex CR manifold \(M\) of hypersurface type, \textit{S. S. Chern} and \textit{J. K. Moser} [Acta Math. 133, 219--271 (1975; Zbl 0302.32015)] and \textit{N. Tanaka} [Jap. J. Math., New Ser. 2, 131--190 (1976; Zbl 0346.32010)] gave two equivalent constructions of a normal Cartan connection \(\Omega\), with values in a principal bundle over \(M\). In the paper under review a very explicit description and proof of this equivalence is given in the case where \(M\) has dimension three. The author also proves that a compact, connected and simply connected strictly pseudoconvex CR manifold of dimension \(3\) that is spherical (i.e. the curvature of \(\Omega\) vanishes everywhere) is CR-diffeomorphic to the sphere \(S^3\) with the standard CR structure.
reviewed by: Andrea Altomani
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 32G07
Mathematics Subject Classification ID: 53C07
zbMATH DE Number: 5189615
zbMATH Keywords: CR manifold
zbMATH Keywords: Cartan connection
MaRDI profile type: Publication
full work available at URL: s00229-006-0070-2
OpenAlex ID: W2010172517
cites work: Q4890970
cites work: A global invariant for three-dimensional CR-manifolds
cites work: Real hypersurfaces in complex manifolds
cites work: Characteristic forms and geometric invariants
cites work: Q3998484
cites work: Q5658761
cites work: Q5731354
cites work: Q4115399
DOI: 10.1007/S00229-006-0070-2
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description: scientific article; zbMATH DE number 5189615