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.
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