Self-dual Einstein Spaces, Heavenly Metrics and Twistors

Abstract : Four-dimensional quaternion-Kahler metrics, or equivalently self-dual Einstein spaces M, are known to be encoded locally into one real function h subject to Przanowski's Heavenly equation. We elucidate the relation between this description and the usual twistor description for quaternion-Kahler spaces. In particular, we show that the same space M can be described by infinitely many different solutions h, associated to different complex (local) submanifolds on the twistor space, and therefore to different (local) integrable complex structures on M. We also study quaternion-Kahler deformations of M and, in the special case where M has a Killing vector field, show that the corresponding variations of h are related to eigenmodes of the conformal Laplacian on M. We exemplify our findings on the four-sphere S^4, the hyperbolic plane H^4 and on the "universal hypermultiplet", i.e. the hypermultiplet moduli space in type IIA string compactified on a rigid Calabi-Yau threefold.
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Article dans une revue
Journal of Mathematical Physics, American Institute of Physics (AIP), 2010, 51, pp.073510. <10.1063/1.3430574>


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Contributeur : Boris Pioline <>
Soumis le : vendredi 18 décembre 2009 - 09:51:19
Dernière modification le : mardi 11 octobre 2016 - 13:25:30

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Sergey Alexandrov, Boris Pioline, Stefan Vandoren. Self-dual Einstein Spaces, Heavenly Metrics and Twistors. Journal of Mathematical Physics, American Institute of Physics (AIP), 2010, 51, pp.073510. <10.1063/1.3430574>. <hal-00442066>

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