62 articles – 637 Notices  [english version]
 HAL : hal-00442066, version 1
 arXiv : 0912.3406
 DOI : 10.1063/1.3430574
 Journal of Mathematical Physics 51 (2010) 073510
 Self-dual Einstein Spaces, Heavenly Metrics and Twistors
 (28/07/2010)
 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.
 Domaine : Physique/Physique des Hautes Energies - Théorie
 Lien vers le texte intégral : http://fr.arXiv.org/abs/0912.3406
 hal-00442066, version 1 http://hal.archives-ouvertes.fr/hal-00442066 oai:hal.archives-ouvertes.fr:hal-00442066 Contributeur : Boris Pioline <> Soumis le : Vendredi 18 Décembre 2009, 09:51:19 Dernière modification le : Lundi 6 Septembre 2010, 16:19:05