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The intrinsic torsion of almost quaternion-Hermitian manifolds

Francisco Martin Cabrera and Andrew Swann
Arxiv ID: 0707.0939Last updated: 11/20/2020
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 Kaehler 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 changes under a twist construction.

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