The intrinsic torsion of almost quaternion-Hermitian manifolds

TY - JOUR

T1 - The intrinsic torsion of almost quaternion-Hermitian manifolds

AU - Martín Cabrera, Francisco

AU - Swann, Andrew

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=50849105399&partnerID=8YFLogxK

U2 - 10.5802/aif.2390

DO - 10.5802/aif.2390

M3 - Journal article

AN - SCOPUS:50849105399

SN - 0373-0956

VL - 58

SP - 1455

EP - 1497

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 5

ER -