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arXiv · 1201.2846

The Calabi-Yau equation for $T^2$-bundles over $\mathbb{T}^2$: the non-Lagrangian case

Ernesto Buzano·Anna Fino·Luigi Vezzoni
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Abstract

In the spirit of [10,2], we study the Calabi-Yau equation on $T^2$-bundles over $\mathbb{T}^2$ 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 $\mathbb{T}^2$ 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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Ernesto Buzano, Anna Fino, Luigi Vezzoni. 2012-03-20. The Calabi-Yau equation for $T^2$-bundles over $\mathbb{T}^2$: the non-Lagrangian case. https://arxiv.org/abs/1201.2846

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