1305.3549 (Dmitri V. Alekseevsky et al.)

Quaternionic Kähler metrics associated with special Kähler manifolds    [PDF]

Dmitri V. Alekseevsky, Vicente Cortés, Malte Dyckmanns, Thomas Mohaupt

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.

View original: http://arxiv.org/abs/1305.3549