Topological canal foliations

Regular canal surfaces of R-3 or S-3 admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of S3 with leaves being canal surfaces, one has to relax the condition "canal" a little ("weak canal condition") in order to accept isolated...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the Mathematical Society of Japan 2019-01, Vol.71 (1), p.43-63
Main Authors: HECTOR, Gilbert, LANGEVIN, Rémi, WALCZAK, Paweł
Format: Article
Language:English
Subjects:
Mathematics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Regular canal surfaces of R-3 or S-3 admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of S3 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.
ISSN:0025-5645
DOI:10.2969/jmsj/78117811