English

Realisation of special Kaehler manifolds as parabolic spheres

Differential Geometry 2007-05-23 v1

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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Cite

@article{arxiv.math/9911079,
  title  = {Realisation of special Kaehler manifolds as parabolic spheres},
  author = {Oliver Baues and Vicente Cortés},
  journal= {arXiv preprint arXiv:math/9911079},
  year   = {2007}
}

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5 pages