The Map Between Conformal Hypercomplex/Hyper-Kähler and Quaternionic(-Kähler) Geometry

Eric Bergshoeff, Sorin Cucu, Tim de Wit, Jos Gheerardyn, Stefan Vandoren, Antoine Van Proeyen

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13 Citaten (Scopus)
107 Downloads (Pure)


We review the general properties of target spaces of hypermultiplets, which are quaternionic-like manifolds, and discuss the relations between these manifolds and their symmetry generators. We explicitly construct a one-to-one map between conformal hypercomplex manifolds (i.e. those that have a closed homothetic Killing vector) and quaternionic manifolds of one quaternionic dimension less. An important role is played by 'ξ-transformations', relating complex structures on conformal hypercomplex manifolds and connections on quaternionic manifolds. In this map, the subclass of conformal hyper-Kähler manifolds is mapped to quaternionic-Kähler manifolds. We relate the curvatures of the corresponding manifolds and furthermore map the symmetries of these manifolds to each other.
Originele taal-2English
Pagina's (van-tot)411-457
Aantal pagina's47
TijdschriftCommunications in Mathematical Physics
StatusPublished - 2006

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