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arXiv · hep-th/0411209

The map between conformal hypercomplex/hyper-Kaehler and quaternionic(-Kaehler) geometry

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

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-Kaehler manifolds is mapped to quaternionic-Kaehler manifolds. We relate the curvatures of the corresponding manifolds and furthermore map the symmetries of these manifolds to each other.

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Eric Bergshoeff, Sorin Cucu, Tim de Wit, Jos Gheerardyn, Stefan Vandoren, Antoine Van Proeyen. 2006-09-15. The map between conformal hypercomplex/hyper-Kaehler and quaternionic(-Kaehler) geometry. https://doi.org/10.1007/s00220-005-1475-6

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