Self-dual Einstein Spaces, Heavenly Metrics and Twistors Auteur(s): Alexandrov S., Pioline Boris, Vandoren Stefan (Article) Publié: Journal Of Mathematical Physics, vol. 51 p.073510 (2010) Texte intégral en Openaccess : Ref HAL: hal-00442066_v1 Ref Arxiv: 0912.3406 DOI: 10.1063/1.3430574 WoS: 000280854500037 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote 14 Citations Résumé: 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. Commentaires: 44 pages, 1 figure |