On transversely holomorphic flows. I
type: Item
instance of: scholarly article
title: On transversely holomorphic flows. I
zbMATH Open document ID: 0873.57021
author: Marco Brunella
published in: Inventiones Mathematicae
publication date: 1997-11-02T00:00:00Z
review text: The paper studies transversely holomorphic one-dimensional orientable foliations on closed connected three-manifolds. Assume that the foliation satisfies a certain rationality condition, for example if \(\dim H^1(M,\mathbb{R})\leq 1\) or if \(H^2(M,{\mathcal O})= 0\), where \(\mathcal O\) is the sheaf of locally constant functions on leaves and transversely holomorphic. Then, the author shows, that the foliation is one of the examples in the following list. (1) Seifert fibrations. (2) Linear foliations on the three-dimensional torus. (3) Strong stable foliations associated to the suspension of hyperbolic diffeomorphisms on the two-dimensional torus. (4) Suspensions of holomorphic automorphisms of the Riemann sphere. (5) Transversely affine foliations on \(S^2\times S^1\). (6) Foliations in \(S^3\) induced by the singularity of holomorphic vector fields in \((\mathbb{C}^2,0)\) which are in the Poincaré domain.
reviewed by: Jesus Muciño Raymundo
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 980764
zbMATH Keywords: 3-manifolds
zbMATH Keywords: linear foliations
zbMATH Keywords: holomorphic
zbMATH Keywords: foliations
zbMATH Keywords: Seifert fibrations
zbMATH Keywords: suspension
MaRDI profile type: Publication
full work available at URL: s002220050098
OpenAlex ID: W1985046940
DOI: 10.1007/S002220050098
description: scientific article; zbMATH DE number 980764