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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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:

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.


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Additional Information

Oliver Baues
Affiliation: Departement Mathematik, ETH-Zentrum, Rämistrasse 101, CH-8092 Zürich, Switzerland
Email: oliver@math.ethz.ch

Vicente Cortés
Affiliation: Mathematisches Institut, Universität Bonn, Beringstraße 1, D-53115 Bonn, Germany
Email: vicente@math.uni-bonn.de

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05981-5
PII: S 0002-9939(00)05981-5
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