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The Quarterly Journal of Mathematics Advance Access originally published online on July 11, 2007
The Quarterly Journal of Mathematics 2007 58(4):443-462; doi:10.1093/qmath/ham030
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

FOUR-DIMENSIONAL CONFORMAL C-SPACES

A. Rod Gover{dagger} and Paul-Andi Nagy {ddagger}

Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

{dagger} Corresponding author. E-mail: gover{at}math.auckland.ac.nz

Received 21 February 2007;
  Abstract

We investigate the structure of conformal C-spaces, a class of Riemannian manifolds which naturally arises as a conformal generalization of the Einstein condition. A basic question is when such a structure is closed, or equivalently locally conformally Cotton. In dimension four, 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.

{ddagger} E-mail: nagy{at}math.auckland.ac.nz


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