2002/05/29 by Oliver Baues, Vicente Cortés
Mathematics · #math.DG #msc:53C26 #msc:53A15
published as Asian J. Math., Vol. 7, No. 1, pp. 115-132, March 2003
arxiv created 2002/05/29 · arxiv updated 2009/11/30
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 \Sr2n+1 \longrightarrow \CPn 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.