Abstract
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.
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