Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A family of Kähler-Einstein manifolds and metric rigidity of Grauert tubes

Author: Róbert Szoke
Journal: Proc. Amer. Math. Soc. 129 (2001), 2913-2917
MSC (2000): Primary 32Q15, 53C35
Published electronically: April 24, 2001
MathSciNet review: 1840093
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In this paper we explain how the so-called adapted complex structures can be used to associate to each compact real-analytic Riemannian manifold a family of complete Kähler-Einstein metrics and show that already one element of this family uniquely determines the original manifold. The underlying manifolds of these metrics are open disc bundles in the tangent bundle of the original Riemannian manifold.

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Additional Information

Róbert Szoke
Affiliation: Department of Analysis, Eötvös University, Kecskeméti u. 10-12, 1053 Budapest, Hungary

Keywords: K\"{a}hler-Einstein metrics, adapted complex structures, Grauert tubes
Received by editor(s): February 2, 2000
Published electronically: April 24, 2001
Communicated by: Mohan Ramachandran
Article copyright: © Copyright 2001 American Mathematical Society