Curvature of almost quaternion-Hermitian manifolds

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 xi and its covariant derivative (del) over tilde xi and determine relations between the decompositions of xi circle times xi, (del) over tilde xi and R. We pay particular attention to the behaviour of the Ricci curvature and the q-Ricci curvature.