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Realisation of special Kähler manifolds as parabolic spheres

Authors: Oliver Baues and Vicente Cortés
Journal: Proc. Amer. Math. Soc. 129 (2001), 2403-2407
MSC (2000): Primary 53A15, 53C26
Published electronically: November 30, 2000
MathSciNet review: 1823925
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Abstract | References | Similar Articles | Additional Information


We prove that any simply connected special Kähler 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 Kähler manifolds with a positive definite metric.

References [Enhancements On Off] (What's this?)

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Additional Information

Oliver Baues
Affiliation: Departement Mathematik, ETH-Zentrum, Rämistrasse 101, CH-8092 Zürich, Switzerland

Vicente Cortés
Affiliation: Mathematisches Institut, Universität Bonn, Beringstraße 1, D-53115 Bonn, Germany

Received by editor(s): November 23, 1999
Published electronically: November 30, 2000
Additional Notes: This work was supported by SFB256 (Universität Bonn)
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society

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