In the spirit of [8, 2], we study the Calabi–Yau equation on T^2-bundles over T^2 endowed with an invariant non-Lagrangian almost-Kähler structure showing that for T^2- invariant initial data it reduces to a Monge–Ampère equation having a unique solution. In this way we prove that for every total space M^4 of an orientable T^2-bundle over T^2 endowed with an invariant almost-Kähler structure the Calabi–Yau problem has a solution for every normalized T^2-invariant volume form.

The Calabi-Yau equation for T^2-bundles over T^2: the non-Lagrangian case

BUZANO, Ernesto;FINO, Anna Maria;VEZZONI, Luigi
2011-01-01

Abstract

In the spirit of [8, 2], we study the Calabi–Yau equation on T^2-bundles over T^2 endowed with an invariant non-Lagrangian almost-Kähler structure showing that for T^2- invariant initial data it reduces to a Monge–Ampère equation having a unique solution. In this way we prove that for every total space M^4 of an orientable T^2-bundle over T^2 endowed with an invariant almost-Kähler structure the Calabi–Yau problem has a solution for every normalized T^2-invariant volume form.
2011
69
281
298
http://arxiv.org/abs/1201.2846
http://arxiv.org/pdf/1201.2846v2.pdf
Almost-Kähler structure; Monge-Ampere equation; T^2-bundle over T^2
E. Buzano; A. Fino; L. Vezzoni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/101147
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