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The Calabi–Yau equation on the Kodaira–Thurston manifold

Part of: Global differential geometry Symplectic geometry, contact geometry

Published online by Cambridge University Press:  24 September 2010

Valentino Tosatti  and
Ben Weinkove
Valentino Tosatti
Affiliation:
Mathematics Department, Columbia University, 2990 Broadway, New York, NY 10027, USA ([email protected])
Ben Weinkove
Affiliation:
Mathematics Department, University of California, San Diego, 9500 Gilman Drive, #0112, La Jolla, CA 92093, USA ([email protected])
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Abstract

We prove that the Calabi–Yau equation can be solved on the Kodaira–Thurston manifold for all given T2-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic 4-manifolds with compatible but non-integrable almost complex structures.

Keywords

Calabi–YauKodaira–Thurston manifoldalmost complexsymplectic

MSC classification

Secondary: 53C99: None of the above, but in this section 53D05: Symplectic manifolds, general
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 10 , Issue 2 , April 2011 , pp. 437 - 447
Copyright
Copyright © Cambridge University Press 2010

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