Curvature of almost quaternion-Hermitian manifolds

Preprint number: CP3-Origins-2010-55
Authors: Francisco Martin Cabrera (University of La Laguna) and Andrew Swann (CP3-Origins)
External link: arXiv.org

Share this pageShare on FacebookTweet about this on TwitterShare on LinkedInGoogle+

Published in Forum Math., vol. 22:1, 21-52, 2010.

We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion ξ and its covariant derivative ~∇ξ and determine relations between the decompositions of ξ⊗ξ, ~∇ξ and R. We pay particular attention to the behaviour of the Ricci curvature and the q-Ricci curvature.