Toric Hermitian surfaces and almost Kähler structures

• Autorzy: Włodzimierz Jelonek
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to investigate the class of compact Hermitian surfaces (M,g,J) admitting an action of the 2-torus T² by holomorphic isometries. We prove that if b₁(M) is even and (M,g,J) is locally conformally Kähler and χ(M) ≠ 0 then there exists an open and dense subset U ⊂ M such that $(U,g_{|U})$ is conformally equivalent to a 4-manifold which is almost Kähler in both orientations. We also prove that the class of Calabi Ricci flat Kähler metrics related with the real Monge-Ampère equation is a subclass of the class of Gibbons-Hawking Ricci flat self-dual metrics.

Kategorie tematyczne

• 53C55: Hermitian and K\"ahlerian manifolds
• 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2007
• Tom: 90
• Numer: 3
• Strony: 203-217

Daty

wydano

2007

Twórcy

autor

Włodzimierz Jelonek

• Institute of Mathematics, Technical University of Cracow, Warszawska 24, 31-155 Kraków, Poland

Identyfikatory

DOI

10.4064/ap90-3-2