The canonical foliation of a compact generalized Hopf manifold
type: Item
instance of: scholarly article
title: The canonical foliation of a compact generalized Hopf manifold
zbMATH Open document ID: 0941.53043
DOI: 10.1016/S0926-2245(99)00018-2
author: K. Tsukada
published in: Differential Geometry and its Applications
publication date: 1999-09-22T00:00:00Z
review text: A locally conformal Kähler manifold \((M,J,g)\) with parallel Lee form \(\omega\) is called a compact generalized Hopf manifold. Set \(\theta=-\omega\circ J\) and denote by \(B\) and \(A\) the dual vector fields corresponding to \(\omega\) and \(\theta\), respectively. Then \(A=JB\). The distribution generated by \(A\) and \(B\) is completely integrable and defines a foliation \(\mathcal F\), which is called the canonical foliation. The author proves the following. (1) One can canonically lift the foliation to any holomorphic line bundle \(F\) on \(M\). Moreover, holomorphic sections of \(F\) are foliated one. (2) The canonical foliation \(\mathcal F\) has a compact leaf. Moreover, he also provides the description of the geometric structure of a compact generalized Hopf manifold on which the canonical foliation is regular.
reviewed by: Bang-Yen Chen
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 1339069
zbMATH Keywords: generalized Hopf manifold
zbMATH Keywords: locally conformal Kähler manifold
zbMATH Keywords: foliation
Wikidata QID: Q115337421
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1339069