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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 41, Pages 2205-2208
http://dx.doi.org/10.1155/S0161171204309038

Mirror symmetry and conformal flatness in general Relativity

1Département de Mathématiques et d'Informatique, Collège Militaire Royal du Canada, Kingston, ON, Canada K7K 5L0
2Département de Mathématiques et de Statistique, Université de Moncton, Moncton, NB, Canada E1A 3E9

Received 4 September 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using symmetry arguments only, we show that every spacetime with mirror-symmetric spatial sections is necessarily conformally flat. The general form of the Ricci tensor of such spacetimes is also determined.