On the Calabi-Yau equation in the Kodaira-Thurston manifold

Luigi Vezzoni. "On the Calabi-Yau equation in the Kodaira-Thurston manifold." Complex Manifolds 3.1 (2016): 239-251. <http://eudml.org/doc/287144>.

@article{LuigiVezzoni2016,
abstract = {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.},
author = {Luigi Vezzoni},
journal = {Complex Manifolds},
keywords = {Calabi-Yau equation; almost-complex structure},
language = {eng},
number = {1},
pages = {239-251},
title = {On the Calabi-Yau equation in the Kodaira-Thurston manifold},
url = {http://eudml.org/doc/287144},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Luigi Vezzoni
TI - On the Calabi-Yau equation in the Kodaira-Thurston manifold
JO - Complex Manifolds
PY - 2016
VL - 3
IS - 1
SP - 239
EP - 251
AB - 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.
LA - eng
KW - Calabi-Yau equation; almost-complex structure
UR - http://eudml.org/doc/287144
ER -