The intrinsic torsion of almost quaternion-Hermitian manifolds

Francisco Martín Cabrera; Andrew Swann

doi:10.5802/aif.2390

The intrinsic torsion of almost quaternion-Hermitian manifolds

Francisco Martín Cabrera^*, Andrew Swann

^*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

18 Citations (Scopus)

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 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 changes under a twist construction.

Original language	English
Journal	Annales de l'Institut Fourier
Volume	58
Issue	5
Pages (from-to)	1455-1497
Number of pages	43
ISSN	0373-0956
DOIs	https://doi.org/10.5802/aif.2390
Publication status	Published - 1 Jan 2008
Externally published	Yes

Keywords

Almost Hermitian structure
Almost quaternion-Hermitian structure
G-connection
G-structure
HKT-manifold
Intrinsic torsion
QKT-manifold

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10.5802/aif.2390

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AB - 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 changes under a twist construction.

KW - Almost Hermitian structure

KW - Almost quaternion-Hermitian structure

KW - G-connection

KW - G-structure

KW - HKT-manifold

KW - Intrinsic torsion

KW - QKT-manifold

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JF - Annales de l'Institut Fourier

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ER -

The intrinsic torsion of almost quaternion-Hermitian manifolds

Abstract

Keywords

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