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 (10)

• Special geometry, cubic polynomials and homogeneous quaternionic spaces
• Special Kahler Manifolds
• String loop corrected hypermultiplet moduli spaces
• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries
• On the hyperkaehler/quaternion Kaehler correspondence
• Linear perturbations of quaternionic metrics
• Twisting Hermitian and hypercomplex geometries
• Completeness in supergravity constructions
• Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence
• Linear perturbations of Hyperkahler metrics

Cited by in corpus (11)

• Symmetries of quaternionic Kähler manifolds with $S^1$-symmetry
• Curvature of quaternionic Kähler manifolds with $S^1$-symmetry
• Solvable groups and a shear construction
• Construction of projective special Kähler manifolds
• Isolated singularities of affine special Kähler metrics in two dimensions
• The c-map on groups
• The c-map as a functor on certain variations of Hodge structure
• Local models of isolated singularities for affine special Kähler structures in dimension two
• The para-HK/QK correspondence
• Symmetries of one-loop deformed q-map spaces
• Special homogeneous surfaces