On sectional curvatures of a Weyl manifold
type: Item
instance of: scholarly article
title: On sectional curvatures of a Weyl manifold
zbMATH Open document ID: 1125.53030
published in: Proceedings of the Japan Academy. Series A
publication date: 2007-06-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1162820091
review text: In [\textit{H. Pedersen} and \textit{K. P. Tod}, Adv. Math. 97, No. 1, 74--109 (1993; Zbl 0778.53041)], it is proved that if \(M\) is a compact positive-definite Einstein-Weyl manifold whose scalar curvature is everywhere strictly negative, then \(M\) is conformal to an Einstein manifold. In this paper, the author shows that if \(M\) is a Weyl manifold, of dimension \(>2\), such that at each point the sectional curvature is independent of the plane chosen, then \(M\) is locally conformal to an Einstein manifold.
reviewed by: Marisa Fernández
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 5161653
zbMATH Keywords: Weyl manifold
zbMATH Keywords: Einstein manifold
zbMATH Keywords: Einstein-Weyl space
zbMATH Keywords: sectional curvature
author: Abdülkadir Özdeğer
MaRDI profile type: Publication
OpenAlex ID: W2098822040
cites work: Q5797637
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cites work: Q4744925
cites work: Three-dimensional Einstein-Weyl geometry
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cites work: On compact conformally flat Einstein-Weyl manifolds
DOI: 10.3792/PJAA.82.123
description: scientific article; zbMATH DE number 5161653