Proper Affine Hyperspheres which fiber over Projective Special Kaehler Manifolds

Details Proper Affine Hyperspheres which fiber over Projective Special Kaehler Manifolds Proper Affine Hyperspheres which fiber over Projective Special Kaehler Manifolds

2002-05-29

arxiv.org/abs/math/0205308v1

Asian J. Math., Vol. 7, No. 1, pp. 115-132, March 2003

Mathematics

Differential Geometry

Scientific paper

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 $\Sr^{2n+1} \longrightarrow \CP^n$ 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.

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