The canonical foliation of a compact generalized Hopf manifold

Let M be a compact generalized Hopf (g.H.) manifold (i.e., a locally conformal Kähler manifold with parallel Lee form) defined by I. Vaisman. We study several properties of the canonical foliation on M. The main results of this paper are the following: 1. (1) We can canonically lift the foliation to...

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Bibliographic Details
Published in:Differential geometry and its applications 1999-07, Vol.11 (1), p.13-28
Main Author: Tsukada, Kazumi
Format: Article
Language:English
Subjects:
canonical foliations
Generalized Hopf manifolds
holomorphic line bundles
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Summary:Let M be a compact generalized Hopf (g.H.) manifold (i.e., a locally conformal Kähler manifold with parallel Lee form) defined by I. Vaisman. We study several properties of the canonical foliation on M. The main results of this paper are the following: 1. (1) We can canonically lift the foliation to any holomorphic line bundle F on M. Moreover holomorphic sections of F are foliated one. 2. (2) There exist compact leaves. 3. (3) We describe the geometric structure of a compact g.H. manifold on which the canonical foliation is regular.
ISSN:0926-2245
1872-6984
DOI:10.1016/S0926-2245(99)00018-2