Publications de l'Institut Mathématique, Nouvelle SérieVol. 94(108), pp. 55–65 (2013)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 94(108), pp. 55–65 (2013) |
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ON THE CONVERSE OF WEYL'S CONFORMAL AND PROJECTIVE THEOREMSGraham HallInstitute of Mathematics, University of Aberdeen, Aberdeen, Scotland, UKAbstract: This note investigates the possibility of converses of the Weyl theorems that two conformally related metrics on a manifold have the same Weyl conformal tensor and that two projectively related connections on a manifold have the same Weyl projective tensor. It shows that, in all relevant cases, counterexamples to each of Weyl's theorems exist except for his conformal theorem in the 4-dimensional, positive definite case, where the converse actually holds. This (conformal) 4-dimensional problem is then solved completely for the other possible signatures. Classification (MSC2000): 53A20, 53A30, 53C50 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 8 Nov 2013. This page was last modified: 22 Nov 2013.
© 2013 Mathematical Institute of the Serbian Academy of Science and Arts
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