Proper Affine Hyperspheres which fiber over Projective Special Kaehler Manifolds
Oliver Baues, Vicente Cortés
Abstract
We show that the natural S1-bundle over a projective special Kaehler manifold carries the geometry of a proper affine hypersphere endowed with a Sasakian structure. The construction generalizes the geometry of the Hopf-fibration 2n+1 n in the context of projective special Kaehler manifolds. As an application we have that a natural circle bundle over the Kuranishi moduli space of a Calabi-Yau threefold is a Lorentzian proper affine hypersphere.
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