Handbook of Pseudo-Riemannian Geometry and Supersymmetry

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pp: 3–13

DOI: 10.4171/079-1/1

Quaternion-Kähler spaces, hyper-Kähler cones, and the c-map

Martin Roček[1], Cumrun Vafa[2] and Stefan Vandoren[3]

(1) Stony Brook University, USA
(2) Harvard University, Cambridge, USA
(3) Universiteit Utrecht, Netherlands

Under the action of the c-map, special Kähler manifolds are mapped into a class of quaternion-Kähler spaces. We explicitly construct the corresponding Swann bundle or hyper-Kähler cone, and determine the hyper-Kähler potential in terms of the prepotencies of the special Kähler geometry.

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