The para-HK/QK correspondence

We generalise the hyper-Kähler/quaternionic Kähler (HK/QK) correspondence to include para-geometries, and present a new concise proof that the target manifold of the HK/QK correspondence is quaternionic Kähler. As an application, we construct one-parameter deformations of the temporal and Euclidean supergravity c-map metrics and show that they are para-quaternionic Kähler.