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