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January, 2019 Topological canal foliations
Gilbert HECTOR, Rémi LANGEVIN, Paweł WALCZAK
J. Math. Soc. Japan 71(1): 43-63 (January, 2019). DOI: 10.2969/jmsj/78117811

Abstract

Regular canal surfaces of $\mathbb{R}^3$ or $\mathbb{S}^3$ admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of $\mathbb{S}^3$ with leaves being canal surfaces, one has to relax the condition “canal” a little (“weak canal condition”) in order to accept isolated umbilics. Here, we define a topological condition which generalizes this “weak canal” condition imposed on leaves, and classify the foliations of compact orientable 3-manifolds we can obtain this way.

Funding Statement

The second and third authors were supported by the Polish NSC grant N$^\circ$ 6065/B/H03/2011/40.

Citation

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Gilbert HECTOR. Rémi LANGEVIN. Paweł WALCZAK. "Topological canal foliations." J. Math. Soc. Japan 71 (1) 43 - 63, January, 2019. https://doi.org/10.2969/jmsj/78117811

Information

Received: 30 May 2017; Published: January, 2019
First available in Project Euclid: 15 October 2018

zbMATH: 07056557
MathSciNet: MR3909914
Digital Object Identifier: 10.2969/jmsj/78117811

Subjects:
Primary: 57R30
Secondary: 53C12

Keywords: canal surface , Foliation , griddling

Rights: Copyright © 2019 Mathematical Society of Japan

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