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Metric geometries over the split quaternions

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  • A. S. Dancer, University of Oxford
  • ,
  • Helge Riis Jørgensen, Department of Mathematics and Computer Science, Denmark
  • A. F. Swann

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.

Original languageEnglish
JournalRendiconti del Seminario Matematico
Pages (from-to)119-139
Number of pages21
Publication statusPublished - 1 Dec 2005
Externally publishedYes

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