The intrinsic torsion of almost quaternion-Hermitian manifolds

Francisco Martín Cabrera[1]; Andrew Swann[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)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 5, page 1455-1497
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Martín Cabrera, Francisco, and Swann, Andrew. "The intrinsic torsion of almost quaternion-Hermitian manifolds." Annales de l’institut Fourier 58.5 (2008): 1455-1497. <http://eudml.org/doc/10354>.

@article{MartínCabrera2008,
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.},
affiliation = {University of La Laguna Department of Fundamental Mathematics 38200 La Laguna Tenerife (Spain); University of Southern Denmark Department of Mathematics and Computer Science Campusvej 55 5230 Odense M (Denmark)},
author = {Martín Cabrera, Francisco, Swann, Andrew},
journal = {Annales de l’institut Fourier},
keywords = {Almost Hermitian structure; almost quaternion-Hermitian structure; $G$-structure; intrinsic torsion; $G$-connection; HKT-manifold; QKT-manifold; almost Hermitian structure; -structure; -connection},
language = {eng},
number = {5},
pages = {1455-1497},
publisher = {Association des Annales de l’institut Fourier},
title = {The intrinsic torsion of almost quaternion-Hermitian manifolds},
url = {http://eudml.org/doc/10354},
volume = {58},
year = {2008},
}

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
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 5
SP - 1455
EP - 1497
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.
LA - eng
KW - Almost Hermitian structure; almost quaternion-Hermitian structure; $G$-structure; intrinsic torsion; $G$-connection; HKT-manifold; QKT-manifold; almost Hermitian structure; -structure; -connection
UR - http://eudml.org/doc/10354
ER -

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