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

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.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: On the Calabi-Yau equation in the Kodaira-Thurston manifold ; volume:3 ; number:1 ; year:2016 ; extent:13 ; Complex manifolds ; 3, Heft 1 (2016) (gesamt 13)

Contributors, Places and Time

• Creator: Vezzoni, Luigi

Further information

• DOI: 10.1515/coma-2016-0012
• URN: urn:nbn:de:101:1-2410281505487.638433576804
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:37 AM CEST