The classification of self-dual Bianchi metrics

Physics

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Scientific paper

Solutions to the self-duality equations, which are invariant under three-dimensional groups of conformal symmetries, are considered. The relationship between the reduced self-duality equation on a metric and the self-duality equation on a Yang - Mills field is established in the context of the symmetry transformation. The main result is the classification of self-dual Bianchi metrics.

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