Toric Hermitian surfaces and almost Kähler structures

Włodzimierz Jelonek. "Toric Hermitian surfaces and almost Kähler structures." Annales Polonici Mathematici 90.3 (2007): 203-217. <http://eudml.org/doc/280844>.

@article{WłodzimierzJelonek2007,
abstract = {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.},
author = {Włodzimierz Jelonek},
journal = {Annales Polonici Mathematici},
keywords = {Hermitian surfaces; toric action; Kähler structure},
language = {eng},
number = {3},
pages = {203-217},
title = {Toric Hermitian surfaces and almost Kähler structures},
url = {http://eudml.org/doc/280844},
volume = {90},
year = {2007},
}

TY - JOUR
AU - Włodzimierz Jelonek
TI - Toric Hermitian surfaces and almost Kähler structures
JO - Annales Polonici Mathematici
PY - 2007
VL - 90
IS - 3
SP - 203
EP - 217
AB - 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.
LA - eng
KW - Hermitian surfaces; toric action; Kähler structure
UR - http://eudml.org/doc/280844
ER -