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
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
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