Normal CR structures on \(S^3\)
type: Item
instance of: scholarly article
title: Normal CR structures on \(S^3\)
zbMATH Open document ID: 1044.32027
author: Florin Belgun
published in: Mathematische Zeitschrift
publication date: 2003-07-01T00:00:00Z
review text: Let \((M,\alpha)\) be a contact manifold of dimension \(2n+1\). \(\alpha\) determines a vector field \(R\), called Reeb vector field, and a contact distribution \(\xi=\text{ker }\alpha\). Given a complex structure \(J:\xi\to \xi\) compatible with \(d\alpha_\xi\) the pair \((J,\xi)\) is called a normal CR structure on \(M\) if \(L_{R\xi }J\equiv 0\) for the Lie derivative. In this paper the author gives the classifications of the normal CR structures on \(S^3\) and their automorphism groups. Combing with results in another paper [Math. Z. 238, No. 3, 441--460 (2001; Zbl 1043.32020)] this completes the classifications of the normal CR structures on compact \(3\)-manifolds. Moreover the author gives a criterion to compare a structure to normal CR structures and shows that the underlying contact structure is unique up to diffeomorphism.
reviewed by: Guangcun Lu
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1944235
zbMATH Keywords: normal CR structures
zbMATH Keywords: Sasakian structures
zbMATH Keywords: contact structures
zbMATH Keywords: compact \(3\)-manifolds
MaRDI profile type: Publication
full work available at URL: s00209-002-0482-y
OpenAlex ID: W1977881133
DOI: 10.1007/S00209-002-0482-Y
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description: scientific article; zbMATH DE number 1944235