On the Einstein-Weyl and conformal self-duality equations

Maciej Dunajski; Eugene Ferapontov; Boris Kruglikov

doi:10.1063/1.4927251

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arXiv · 1406.0018

On the Einstein-Weyl and conformal self-duality equations

Maciej Dunajski·Eugene Ferapontov·Boris Kruglikov

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Abstract

The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as `master dispersionless systems' in four and three dimensions respectively. Their integrability by twistor methods has been established by Penrose and Hitchin. In this note we present, in specially adapted coordinate systems, explicit forms of the corresponding equations and their Lax pairs. In particular, we demonstrate that any Lorentzian Einstein-Weyl structure is locally given by a solution to the Manakov-Santini system, and we find a system of two coupled third-order scalar PDEs for a general anti-self-dual conformal structure in neutral signature.

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nlin.SI gr-qc hep-th math.DG

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Maciej Dunajski, Eugene Ferapontov, Boris Kruglikov. 2014-05-30. On the Einstein-Weyl and conformal self-duality equations. https://doi.org/10.1063/1.4927251

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