1999/11/11 by Oliver Baues, Vicente Cortés
Mathematics · #math.DG #msc:53C26 #msc:53A15
published as Proc. Am. Math. Soc. 129:8 (2001), pp. 2403-2407 · 5 pages
arxiv created 1999/11/11 · arxiv updated 2009/11/30
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.