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

Realisation of special Kähler manifolds as parabolic spheres