Twist geometry of the c-map

Abstract

We discuss the geometry of the c-map from projective special Kähler to quaternionic Kähler manifolds using the twist construction to provide a global approach to Hitchin's description. As found by Alexandrov et al. and Alekseevsky et al. this is related to the quaternionic flip of Haydys. We prove uniqueness statements for several steps of the construction. In particular, we show that given a hyperKähler manifold with a rotating symmetry, there is essentially only a one parameter degree of freedom in constructing a quaternionic Kähler manifold of the same dimension. We demonstrate how examples on group manifolds arise from this picture.

34 pages, references corrected

References in corpus (3)

• String loop corrected hypermultiplet moduli spaces
• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries
• Linear perturbations of Hyperkahler metrics