## The Calabi–Yau equation on 4-manifolds over 2-tori

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- by A. Fino, Y.Y. Li, S. Salamon and L. Vezzoni PDF
- Trans. Amer. Math. Soc.
**365**(2013), 1551-1575 Request permission

## Abstract:

This paper pursues the study of the Calabi–Yau equation on certain symplectic non-Kähler 4-manifolds, building on a key example of Tosatti and Weinkove in which more general theory had proved less effective. Symplectic 4-manifolds admitting a 2-torus fibration over a 2-torus base $\mathbb {T}^2$ are modelled on one of three solvable Lie groups. Having assigned an invariant almost-Kähler structure and a volume form that effectively varies only on $\mathbb {T}^2$, one seeks a symplectic form with this volume. Our approach simplifies the previous analysis of the problem and establishes the existence of solutions in various other cases.## References

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## Additional Information

**A. Fino**- Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italia
- MR Author ID: 363840
- ORCID: 0000-0003-0048-2970
- Email: annamaria.fino@unito.it
**Y.Y. Li**- Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854
- Email: yyli@math.rutgers.edu
**S. Salamon**- Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italia – and – Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, United Kingdom
- Email: simon.salamon@kcl.ac.uk
**L. Vezzoni**- Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italia
- Email: luigi.vezzoni@unito.it
- Received by editor(s): April 11, 2011
- Received by editor(s) in revised form: August 6, 2011
- Published electronically: October 1, 2012
- © Copyright 2012 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**365**(2013), 1551-1575 - MSC (2010): Primary 53C25, 35J60, 53D35
- DOI: https://doi.org/10.1090/S0002-9947-2012-05692-3
- MathSciNet review: 3003274