On toric locally conformally Kähler manifolds

被引:0
作者
Farid Madani
Andrei Moroianu
Mihaela Pilca
机构
[1] Goethe Universität Frankfurt,Institut für Mathematik
[2] Université Paris-Saclay,Laboratoire de Mathématiques de Versailles, UVSQ, CNRS
[3] Universität Regensburg,Fakultät für Mathematik
[4] Institute of Mathematics “Simion Stoilow” of the Romanian Academy,undefined
来源
Annals of Global Analysis and Geometry | 2017年 / 51卷
关键词
Locally conformally Kähler structure; Hopf surface; Toric manifold; Twisted Hamiltonian; 53A30; 53B35; 53C25; 53C29; 53C55;
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学科分类号
摘要
We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is -∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\infty $$\end{document}, and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold.
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页码:401 / 417
页数:16
相关论文
共 32 条
  • [1] Belgun FA(2000)On the metric structure of non-Kähler complex surfaces Math. Ann. 317 1-40
  • [2] Carrell J(1973)Holomorphic vector fields on complex surfaces Math. Ann. 204 73-81
  • [3] Howard A(2001)Surfaces de la classe VII admettant un champ de vecteurs, II Comment. Math. Helv. 76 640-664
  • [4] Kosniowski C(1984)La Math. Ann. 267 495-518
  • [5] Dloussky G(1998)-forme de torsion d’une variété hermitienne compacte Ann. Inst. Fourier 48 1107-1127
  • [6] Oeljeklaus K(1974)Locally conformally Kähler metrics on Hopf surfaces Invent. Math. 24 269-310
  • [7] Toma M(1980)On Surfaces of Class VII Kodai Math. J. 3 70-82
  • [8] Gauduchon P(1980)On V-harmonic forms in compact locally conformal Kähler manifolds with the parallel Lee form Ann. Fac. Sci. Univ. Nat. Zaïre (Kinshasa) 6 17-29
  • [9] Gauduchon P(1960)On harmonic forms in compact locally conformal Kähler manifolds with the parallel Lee form Ann. Math. 71 111-152
  • [10] Ornea L(1963)On compact complex analytic spaces I ibid 77 563-626