Session 29. Quaternion-Kähler manifolds and related structures in Riemannian and algebraic geometry

HK/QK correspondence and the c-map

Malte Dyckmanns, Universität Hamburg, Germany
The HK/QK correspondence associates a one-parameter family of quaternionic (pseudo-)Kähler manifolds to any (pseudo-)hyper-Kähler manifold with rotating Killing vector field (i.e. a Killing vector field that preserves one complex structure while rotating the other two). We consider examples of this correspondence with particular emphasis on quaternionic Kähler manifolds coming from the physicists' ``c-map'' construction.
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