Metric geometries over the split quaternions

TY - JOUR

T1 - Metric geometries over the split quaternions

AU - Dancer, A. S.

AU - Jørgensen, Helge Riis

AU - Swann, A. F.

PY - 2005/12/1

Y1 - 2005/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33751538018&partnerID=8YFLogxK

M3 - Review

AN - SCOPUS:33751538018

SN - 0373-1243

VL - 63

SP - 119

EP - 139

JO - Rendiconti del Seminario Matematico

JF - Rendiconti del Seminario Matematico

IS - 2

ER -