Necessary and sufficient conditions for (i) Weyl, (ii) Riemann-Cartan connections
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for (i) Weyl, (ii) Riemann-Cartan connections
zbMATH Open document ID: 0799.53016
DOI: 10.1016/0393-0440(94)90034-5
author: S. Brian Edgar
published in: Journal of Geometry and Physics
publication date: 1994-08-21T00:00:00Z
review text: For a space with metric \(h_{ab}\) its semimetric connection defined by \(\nabla_ c h_{ab}= h_{ab}\lambda_ c\) necessarily satisfies an algebraic relation of the type \(h_{ai}\breve R^ i_{bcd}+h_{bi}\breve R^ i_{acd}=0\), where \(\breve R^ i_{bcd}\) is related to the curvature tensor \(R^ i_{bcd}\) of the Euclidean connection by \(\breve R^ i_{bcd}=R^ i_{bcd}-{1\over 2}\delta^ a_ bR^ i_{icd}\). For a four-dimensional space time, in particular, it is shown that this relationship also provides a sufficient condition for the local existence of a curvature tensor of a semi-metric connection.
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 569289
zbMATH Keywords: semimetric connection
zbMATH Keywords: curvature tensor
reviewed by: Tanjiro Okubo
MaRDI profile type: Publication
full work available at URL: 0393-0440(94)90034-5
OpenAlex ID: W1966691260
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description: scientific article; zbMATH DE number 569289