The intrinsic torsion of almost quaternion-Hermitian manifolds

TL;DR

This paper investigates the intrinsic torsion of almost quaternion-Hermitian manifolds using exterior algebra, providing practical computation methods, characterizations of special geometries, and analyzing the effects of twist constructions.

Contribution

It introduces a new exterior algebra approach to determine intrinsic torsion and characterizes HKT and QKT geometries in this framework.

Findings

Intrinsic torsion determined by three-forms from exterior derivatives of Kaehler forms.

Practical method for computing intrinsic torsion.

Characterizations of HKT and QKT geometries in exterior algebra.

Abstract

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.