English

Proper Affine Hyperspheres which fiber over Projective Special Kaehler Manifolds

Differential Geometry 2007-05-23 v1

Abstract

We show that the natural S^1-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\CPn\Sr^{2n+1} \longrightarrow \CP^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.

Keywords

Cite

@article{arxiv.math/0205308,
  title  = {Proper Affine Hyperspheres which fiber over Projective Special Kaehler Manifolds},
  author = {Oliver Baues and Vicente Cortés},
  journal= {arXiv preprint arXiv:math/0205308},
  year   = {2007}
}