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This article examines the coincidence of the projective and conformal Weyltensors associated to a given connection D. The connection may be a generalWeyl connection associated to a conformal class of metrics [g]. The main resultfor n>3 is that the Weyl tensors coincide iff D is the Levi-Civita connectionof an Einstein metric.

A note on the coincidence of the projective and conformal Weyl tensors