Curvature of almost quaternion-Hermitian manifolds

Abstract

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 and determine relations between the decompositions of ξ ⊗ ξ, and R. We pay particular attention to the behaviour of the Ricci curvature and the q-Ricci curvature.