Almost Quaternion-Hermitian Manifolds

Original · EN

Following the point of view of Gray and Hervella, we derive detailed conditions which characterize each one of the classes of almost quaternion-Hermitian 4n-manifolds, n>1. Previously, by completing a basic result of A. Swann, we give explicit descriptions of the tensors contained in the space of covariant derivatives of the fundamental form Ω and split the coderivative of Ω into its Sp(n) Sp(1)-components. For 4n>8, A. Swann also proved that all the information about the intrinsic torsion ∇ Ω is contained in the exterior derivative d Ω. Thus, we give alternative conditions, expressed in terms of d Ω, to characterize the different classes of almost quaternion-Hermitian manifolds.