Abstract
We study the integrability of the Einstein equations for a class of empty homogeneous space-times (Bianchi class A), once the self-duality constraints are imposed on the space-time itself. This system is integrable in the case of Bianchi type I and is a subset of Bianchi types VI0 and VII0. Bianchi type II space-times do not admit self-dual solutions and for the case of Bianchi VIII and IX we were unable to find a general integrability condition.
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