Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Topological canal foliations
Gilbert HectorRémi LangevinPaweł Walczak
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2019 Volume 71 Issue 1 Pages 43-63

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Abstract

Regular canal surfaces of ℝ3 or 𝕊3 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.

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© 2019 The Mathematical Society of Japan
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