6533b871fe1ef96bd12d2652
RESEARCH PRODUCT
Topological canal foliations
Rémi LangevinGilbert HectorPaweł Walczaksubject
rational parametrizationsQuantitative Biology::Tissues and OrgansGeneral MathematicsPhysics::Medical PhysicssurfacesTopology01 natural sciencesQuantitative Biology::Cell Behavior0103 physical sciencesotorhinolaryngologic diseases57R30[MATH]Mathematics [math]0101 mathematicsMathematicsEnvelope (waves)griddlingQuantitative Biology::Molecular Networks010102 general mathematicsOrder (ring theory)53C12foliationFoliation (geology)sense organsMathematics::Differential Geometry010307 mathematical physicscanal surfacedescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-01-01 | Journal of the Mathematical Society of Japan |