Title: Necessary and sufficient conditions for (i) Weyl, (ii) Riemann-Cartan connections
Abstract: Spaces with semi-metric connections (which include metric, Weyl and Riemann-Cartan connections), defined by ▿chab=habλc, necessarily satisfy an algebraic relationship of the type haiŘibcd+hbiŘiacd=0, where hab is a metric tensor, and Řabcd is related to the curvature tensor Rabcd of the connection by Řabcd=Rabcd−14δabRiicd. It is shown—in a four-dimensional spacetime, for almost all curvature tensors—that this algebraic relationship is also a sufficient condition for the local existence of a curvature tensor of a semi-metric connection. Generalisations of this result, involving a tensor more general than the curvature tensor, are also given.
Publication Year: 1994
Publication Date: 1994-04-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 4
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