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Some remarks on quaternion-Hermitian manifolds

Andrew Swann — 1997

Archivum Mathematicum

Nearly-quaternionic Kähler manifolds of dimension at least  8 are shown to be quaternionic Kähler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic Kähler are also found.

The hyperKähler geometry associated to Wolf spaces

Piotr KobakAndrew Swann — 2001

Bollettino dell'Unione Matematica Italiana

Sia G un grupo di Lie compatto e semplice. Sia O min la più piccola orbita nilpotente non-banale nell'algebra di Lie complessa g C . Si presenta una costruzione diretta di teoria di Lie delle metriche iperKahler su O min con potenziale Kahleriano G -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).

The intrinsic torsion of almost quaternion-Hermitian manifolds

Francisco Martín CabreraAndrew Swann — 2008

Annales de l’institut Fourier

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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