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

Luigi Vezzoni

Complex Manifolds (2016)

  • Volume: 3, Issue: 1, page 239-251
  • ISSN: 2300-7443

Abstract

top
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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.