no. 5
The intrinsic torsion of almost quaternion-Hermitian manifolds
[La torsion intrinsèque des variétés presque hermitiennes quaternioniennes]
Martín Cabrera, Francisco1 ; Swann, Andrew2
1 University of La Laguna Department of Fundamental Mathematics 38200 La Laguna Tenerife (Spain)
2 University of Southern Denmark Department of Mathematics and Computer Science Campusvej 55 5230 Odense M (Denmark)
Annales de l'Institut Fourier, Tome 58 (2008) no. 5, pp. 1455-1497.

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.

DOI : 10.5802/aif.2390
Classification : 53C15, 53C10, 53C26, 53C80
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

Martín Cabrera, Francisco 1 ; Swann, Andrew 2

1 University of La Laguna Department of Fundamental Mathematics 38200 La Laguna Tenerife (Spain)
2 University of Southern Denmark Department of Mathematics and Computer Science Campusvej 55 5230 Odense M (Denmark) 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2390/

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