Metric geometries over the split quaternions

Journal article

We give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaternionic Kähler metrics from indefinite real analytic conformal manifolds. We also indicate how the theory of toric varieties gives rise to constructions of hypersymplectic manifolds.

Authors: Dancer, A; Jørgensen, H; Swann, A

• Journal: Rendiconti del Seminario Matematico
• Volume: 63
• Issue: 2
• Pages: 119-139
• Publication date: 2005-01-01
• ISSN: 0373-1243