Special geometries associated to quaternion-Kähler 8-manifolds

We develop a calculus of differential forms on a quaternion-Kähler manifold M4nM4n admitting an isometric circle action. This is used to study three fundamental examples of such actions on the quaternionic projective plane and the construction of G2G2 and half-flat structures on quotients of M8M8 and its hypersurfaces.