Metric geometries over the split quaternions

Details Metric geometries over the split quaternions Metric geometries over the split quaternions

2004-12-10

arxiv.org/abs/math/0412215v1

Mathematics

Differential Geometry

23 pages

Scientific paper

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

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