Four dimensional conformal C-spaces

A.Rod Gover and Paul-Andi Nagy


We investigate the structure of conformal C-spaces, a class of Riemannian manifolds which naturally arises as a conformal generalisation of the Einstein condition. A basic question is when such a structure is closed, or equivalently locally conformally Cotton. In dimension 4 we obtain a full answer to this question and also investigate the incidence of the Bach condition on this class of metrics. This is related to earlier results obtained in the Einstein-Weyl context.

Conformal C-space, Einstein metric, Weyl tensor

Math Review Classification
Primary 53A30, 53C24, 53C55

Last Updated
22 January 2007

19 pages

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