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On the Einstein-Weyl and conformal self-duality equations

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posted on 2015-11-05, 14:50 authored by M. Dunajski, Evgeny FerapontovEvgeny Ferapontov, B. Kruglikov
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 partial differential equations for a general anti-self-dual conformal structure in neutral signature.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

JOURNAL OF MATHEMATICAL PHYSICS

Volume

56

Issue

8

Pages

? - ? (10)

Citation

DUNAJSKI, M., FERAPONTOV, E.V. and KRUGLIKOV, B., 2015. On the Einstein-Weyl and conformal self-duality equations. Journal of Mathematical Physics, 56, 083501, DOI: 10.1063/1.4927251

Publisher

© AIP Publishing LLC.

Version

  • VoR (Version of Record)

Publication date

2015

Notes

Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics 56, 083501 (2015) and may be found at http://scitation.aip.org/content/aip/journal/jmp/56/8/10.1063/1.4927251.

ISSN

1086-7658

Language

  • en

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