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The identification of conformal hypercomplex and quaternionic manifolds

Eric Bergshoeff·Stefan Vandoren·Antoine Van Proeyen
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Abstract

We review the map between hypercomplex manifolds that admit a closed homothetic Killing vector (i.e. `conformal hypercomplex' manifolds) and quaternionic manifolds of 1 dimension less. This map is related to a method for constructing supergravity theories using superconformal techniques. An explicit relation between the structure of these manifolds is presented, including curvatures and symmetries. An important role is played by `ξtransformations', relating connections on quaternionic manifolds, and a new type `\hatξtransformations' relating complex structures on conformal hypercomplex manifolds. In this map, the subclass of conformal hyper-Kaehler manifolds is mapped to quaternionic-Kaehler manifolds.

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Eric Bergshoeff, Stefan Vandoren, Antoine Van Proeyen. 2005-12-04. The identification of conformal hypercomplex and quaternionic manifolds. https://doi.org/10.1142/s0219887806001521

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