We review some previous results about the Calabi-Yau equation on the Kodaira-Thurston manifold equipped with an invariant almost-Kähler structure and assuming the volume form T2-invariant. In particular, we observe that under some restrictions the problem is reduced to aMonge-Ampère equation by using the ansatz ˜~ω = Ω− dJdu + da, where u is a T2-invariant function and a is a 1-form depending on u. Furthermore, we extend our analysis to non-invariant almost-complex structures by considering some basic cases and we finally take into account a generalization to higher dimensions.
@article{bwmeta1.element.doi-10_1515_coma-2016-0012,
author = {Luigi Vezzoni},
title = {On the Calabi-Yau equation in the Kodaira-Thurston manifold},
journal = {Complex Manifolds},
volume = {3},
year = {2016},
zbl = {1354.32018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2016-0012}
}
Luigi Vezzoni. On the Calabi-Yau equation in the Kodaira-Thurston manifold. Complex Manifolds, Tome 3 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2016-0012/