Realisation of special Kähler manifolds as parabolic spheres
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- by Oliver Baues and Vicente Cortés PDF
- Proc. Amer. Math. Soc. 129 (2001), 2403-2407 Request permission
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2403-2407
- MSC (2000): Primary 53A15, 53C26
- DOI: https://doi.org/10.1090/S0002-9939-00-05981-5
- MathSciNet review: 1823925