Quaternionic Kähler metrics associated with special Kähler manifolds

Abstract

We give an explicit formula for the quaternionic Kähler 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 Kähler. A similar explicit formula is given for the analogous (K/K) correspondence between Kähler manifolds endowed with a Hamiltonian Killing vector field. As an example, we apply this formula in the case of an arbitrary conical Kähler manifold.

30 pages, appendix extended, final version published in JGP

References in corpus (6)

• Sasaki-Einstein Manifolds and Volume Minimisation
• String loop corrected hypermultiplet moduli spaces
• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries
• Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
• On the hyperkaehler/quaternion Kaehler correspondence
• Proper Affine Hyperspheres which fiber over Projective Special Kaehler Manifolds

Cited by in corpus (28)

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• Isometries, gaugings and N=2 supergravity decoupling
• Curvature of quaternionic Kähler manifolds with $S^1$-symmetry
• Four-dimensional geometric supergravity and electromagnetic duality: a brief guide for mathematicians
• Construction of projective special Kähler manifolds
• ASK/PSK-correspondence and the r-map
• Isolated singularities of affine special Kähler metrics in two dimensions
• Einstein metrics on bundles over hyperKähler manifolds
• The quaternionic/hypercomplex-correspondence
• The c-map as a functor on certain variations of Hodge structure
• Elementary deformations and the hyperKähler-quaternionic Kähler correspondence
• Complete quaternionic Kähler manifolds with finite volume ends
• The para-HK/QK correspondence
• S-duality and the universal isometries of instanton corrected q-map spaces
• Curvature of quaternionic skew-Hermitian manifolds and bundle constructions
• A class of locally inhomogeneous complete quaternionic Kähler manifolds
• Twist, elementary deformation, and KK correspondence in generalized complex geometry
• Heisenberg-invariant self-dual Einstein manifolds
• Manifolds with holonomy U*(2m)
• Quaternion-Kähler manifolds near maximal fixed points sets of $S^1$-symmetries
• An analogue of the Gibbons-Hawking Ansatz for quaternionic Kähler spaces
• Symmetries of one-loop deformed q-map spaces
• Special homogeneous surfaces
• S-duality and the universal isometries of q-map spaces
• Special Geometry of Euclidean Supersymmetry IV: the local c-map