Compact Einstein-Weyl manifolds with large symmetry group
type: Item
instance of: scholarly article
title: Compact Einstein-Weyl manifolds with large symmetry group
zbMATH Open document ID: 0881.53041
DOI: 10.1215/S0012-7094-97-08817-7
author: Anders Bisbjerg Madsen
author: Henrik Pedersen
author: Yat-Sun Poon
author: Andrew Swann
published in: Duke Mathematical Journal
publication date: 1998-02-19T00:00:00Z
review text: The authors give a classification of 4-dimensional compact Einstein-Weyl manifolds whose symmetry group is at least 4-dimensional. A Weyl geometry consists of a conformal class \([g]\) of metrics and a connection \(D\) such that for all \(g\in [g]\) there exists a 1-form \(\omega\) with \(Dg= \omega \otimes g\). From reading the proof of Lemma 2.2 it seems that the authors restrict their consideration to positive signature \((+,+,+,+)\). An Einstein-Weyl manifold is a Weyl geometry such that \(Sr^D= \Lambda g\), where \(Sr^D\) is the symmetrization of the Ricci tensor and \(\Lambda\) is a constant.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 1042490
zbMATH Keywords: Einstein-Weyl manifolds
zbMATH Keywords: symmetry group
zbMATH Keywords: Weyl geometry
zbMATH Keywords: Ricci tensor
reviewed by: Marcus Kriele
MaRDI profile type: Publication
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full work available at URL: s0012-7094-97-08817-7
OpenAlex ID: W1964877332
description: scientific article; zbMATH DE number 1042490