Proceedings of the American Mathematical Society

Author(s): Oliver Baues; Vicente Cortés
Journal: Proc. Amer. Math. Soc. 129 (2001), 2403-2407.
MSC (2000): Primary 53A15, 53C26
Posted: November 30, 2000
Retrieve article in: PDF DVI PostScript
This article is available free of charge

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.

[ACD]: D.V. Alekseevsky, V. Cortés, C. Devchand, Special complex manifolds, math.DG/9910091, ESI preprint 779.
[B]: W. Blaschke, Vorlesungen über Differentialgeometrie II. Affine Differentialgeometrie, Grundlehren der Mathematischen Wissenschaften VII, Springer Verlag, Berlin 1923.
[C]: V. Cortés, On hyper-Kähler manifolds associated to Lagrangian Kähler submanifolds of $T\sp *{C}\sp n$ , Trans. Amer. Math. Soc. 350 (1998), no. 8, 3193-3205. MR 98k:53059
[F]: D.S. Freed, Special Kähler manifolds, Comm. Math. Phys. 203 (1999), no. 1, 31-52. MR 2000f:53060
[L]: Zhiqin Lu, A note on special Kähler manifolds, Math. Ann. 313 (1999), no. 4, 711-713. MR 2000f:53061
[NS]: K. Nomizu, T. Sasaki, Affine differential geometry. Geometry of affine immersions, Cambridge Tracts in Mathematics 111, Cambridge University Press, Cambridge, 1994. MR 96e:53014

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53A15, 53C26

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: 10.1090/S0002-9939-00-05981-5
PII: S 0002-9939(00)05981-5
Received by editor(s): November 23, 1999
Posted: November 30, 2000
Additional Notes: This work was supported by SFB256 (Universität Bonn)
Communicated by: Christopher Croke
Copyright of article: Copyright 2000, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS