[La torsion intrinsèque des variétés presque hermitiennes quaternioniennes]
Nous étudions la torsion intrinsèque des variétés presque hermitiennes quaternioniennes via l’algèbre extérieur. En particulier, nous montrons comment elle est déterminée par trois-formes particulières, formées à partir de simples combinaisons des différentielles extérieures des formes kählériennes locales. Ceci donne une méthode pratique pour calculer la torsion intrinsèque qui s’applique dans de nombreux exemples. En plus, nous trouvons des caractérisations simples des géométries HKT et QKT en utilisant l’algèbre extérieur et nous calculons la modification de la torsion intrinsèque pour une construction twistée.
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.
Keywords: Almost Hermitian structure, almost quaternion-Hermitian structure, $G$-structure, intrinsic torsion, $G$-connection, HKT-manifold, QKT-manifold
Mot clés : structure presque hermitienne, structure presque hermitienne quaternionienne, $G$-structure, torsion intrinsèque, $G$-connexion, HKT-variété, QKT-variété
@article{AIF_2008__58_5_1455_0,
author = {Mart{\'\i}n Cabrera, Francisco and Swann, Andrew},
title = {The intrinsic torsion of almost {quaternion-Hermitian} manifolds},
journal = {Annales de l'Institut Fourier},
pages = {1455--1497},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {58},
number = {5},
year = {2008},
doi = {10.5802/aif.2390},
zbl = {1145.53017},
mrnumber = {2445825},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.2390/}
}
TY - JOUR AU - Martín Cabrera, Francisco AU - Swann, Andrew TI - The intrinsic torsion of almost quaternion-Hermitian manifolds JO - Annales de l'Institut Fourier PY - 2008 SP - 1455 EP - 1497 VL - 58 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2390/ DO - 10.5802/aif.2390 LA - en ID - AIF_2008__58_5_1455_0 ER -
%0 Journal Article %A Martín Cabrera, Francisco %A Swann, Andrew %T The intrinsic torsion of almost quaternion-Hermitian manifolds %J Annales de l'Institut Fourier %D 2008 %P 1455-1497 %V 58 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2390/ %R 10.5802/aif.2390 %G en %F AIF_2008__58_5_1455_0
Martín Cabrera, Francisco; Swann, Andrew. The intrinsic torsion of almost quaternion-Hermitian manifolds. Annales de l'Institut Fourier, Tome 58 (2008) no. 5, pp. 1455-1497. doi : 10.5802/aif.2390. http://archive.numdam.org/articles/10.5802/aif.2390/
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