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

• Autorzy: Luigi Vezzoni
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32Q60: Almost complex manifolds
• 32Q25: Calabi-Yau theory
• 35J60: Nonlinear elliptic equations

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2016
• Tom: 3
• Numer: 1

Daty

otrzymano

2016-06-30

zaakceptowano

2016-09-01

online

2016-10-07

Twórcy

autor

Luigi Vezzoni

• Dipartimento di Matematica G. Peano, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

Identyfikatory

DOI

10.1515/coma-2016-0012