Hyper Kähler and quaternionic Kähler geometry.
Singular Moment Maps and Quaternionic Geometry
Some remarks on quaternion-Hermitian manifolds
Nearly-quaternionic Kähler manifolds of dimension at least are shown to be quaternionic Kähler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic Kähler are also found.
Einstein-Weyl geometry, the Bach tensor and conformal scalar curvature.
The hyperKähler geometry associated to Wolf spaces
Sia un grupo di Lie compatto e semplice. Sia la più piccola orbita nilpotente non-banale nell'algebra di Lie complessa . Si presenta una costruzione diretta di teoria di Lie delle metriche iperKahler su con potenziale Kahleriano -invariante e compatibili con la forma simplettica complessa di Kostant-Kirillov-Souriau. In particolare si ottengono le metriche iperKahler dei fibrati associati sugli spazi di Wolf (spazi simmetrici quaternionali a curvatura scalare positiva).
Quaternionic geometry of a nilpotent variety.
The intrinsic torsion of almost quaternion-Hermitian manifolds
We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local Kähler forms. This gives a practical method to compute the intrinsic torsion and is applied in a number of examples. In addition we find simple characterisations of HKT and QKT geometries entirely in the exterior algebra and compute how the intrinsic torsion...
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