Publications de l'Institut Mathématique, Nouvelle Série Vol. 94(108), pp. 55–65 (2013) 

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 4dimensional, positive definite case, where the converse actually holds. This (conformal) 4dimensional 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)
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