Quaternionic K\"ahler metrics associated with special K\"ahler manifolds

Understand

We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence.

• As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic K\"ahler.
• A similar explicit formula is given for the analogous (K/K) correspondence between K\"ahler manifolds endowed with a Hamiltonian Killing vector field.
• As an example, we apply this formula in the case of an arbitrary conical K\"ahler manifold.