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Realisation of special Kaehler manifolds as parabolic spheres

Oliver Baues·Vicente Cortés
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Abstract

We prove that any simply connected special Kaehler manifold admits a canonical immersion as a parabolic affine hypersphere. As an application, we associate a parabolic affine hypersphere to any nondegenerate holomorphic function. Also we show that a classical result of Calabi and Pogorelov on parabolic spheres implies Lu's theorem on complete special Kaehler manifolds with a positive definite metric.

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Oliver Baues, Vicente Cortés. 1999-11-11. Realisation of special Kaehler manifolds as parabolic spheres. https://arxiv.org/abs/math/9911079

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