Toric Hermitian surfaces and almost Kähler structures

W/lodzimierz Jelonek¹

¹ Institute of Mathematics Technical University of Cracow Warszawska 24 31-155 Kraków, Poland

Annales Polonici Mathematici, Tome 90 (2007) no. 3, pp. 203-217

Résumé

The aim of this paper is to investigate the class of compact Hermitian surfaces $(M,g,J)$ admitting an action of the 2-torus $T^2$ by holomorphic isometries. We prove that if $b_1(M)$ is even and $(M,g,J)$ is locally conformally Kähler and $\chi (M)\not =0$ then there exists an open and dense subset $U\subset M$ 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.

Détail

DOI : 10.4064/ap90-3-2

Keywords: paper investigate class compact hermitian surfaces admitting action torus holomorphic isometries prove even locally conformally hler chi there exists dense subset subset conformally equivalent manifold which almost hler orientations prove class calabi ricci flat hler metrics related real monge amp equation subclass class gibbons hawking ricci flat self dual metrics