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

OnderzoeksoutputAcademicpeer review

13 Citaten (Scopus)
107 Downloads (Pure)

Samenvatting

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
Volume262
DOI's
StatusPublished - 2006

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