The canonical foliations of a locally conformal Kähler manifold
type: Item
instance of: scholarly article
title: The canonical foliations of a locally conformal Kähler manifold
zbMATH Open document ID: 0587.53059
DOI: 10.1007/BF01763178
author: Paolo Piccinni
author: Bang-Yen Chen
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1985-01-01T00:00:00Z
review text: Three canonical foliations of a locally conformal Kähler manifold M are defined, and their properties studied. A fourth canonical foliation is defined when the Lee form of M is parallel. All of these foliations are totally geodesic and Riemannian. One of them is almost complex. If the almost complex foliation is regular, and if M is compact, it is proved that M fibers over a compact Kähler manifold with the fibers being totally geodesic flat tori. Finally the geometrical properties, the canonical class, and the Godbillon-Vey class of the totally real foliation of a CR-submanifold are studied. This paper extends the work of I. Vaisman on locally conformal Kähler manifolds and generalized Hopf manifolds.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 3942421
zbMATH Keywords: Lee form
zbMATH Keywords: totally geodesic foliation
zbMATH Keywords: Riemannian foliation
zbMATH Keywords: Kähler manifold
zbMATH Keywords: CR-submanifold
zbMATH Keywords: Hopf manifolds
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01763178
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description: scientific article; zbMATH DE number 3942421