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math.DG2004★ 7 cited
Metric geometries over the split quaternions
A. S. Dancer, H. R. Jorgensen, A. F. Swann
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 di…
math.DG2004★ 2 cited
Toric Hypersymplectic Quotients
Andrew Dancer, Andrew Swann
We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R^{4d} by the action of a compact Abelian group. These 4n-dimensional quotients carry a mult…
math.DG1998
Quaternionic Kähler Manifolds of Cohomogeneity One
Andrew Dancer, Andrew Swann
Classification results are given for (i) compact quaternionic Kähler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperKähler manifolds w…