Realisation of special Kaehler manifolds as parabolic spheres

Details Realisation of special Kaehler manifolds as parabolic spheres Realisation of special Kaehler manifolds as parabolic spheres

1999-11-11

arxiv.org/abs/math/9911079v1

Proc. Am. Math. Soc. 129:8 (2001), pp. 2403-2407

Mathematics

Differential Geometry

5 pages

Scientific paper

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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