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In mathematics, the Reeb foliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1993).
It is based on dividing the sphere into two solid tori, along a 2-torus: see Clifford torus. Each of the solid tori is then foliated internally, in codimension 1, and the dividing torus surface forms one more leaf.
By Novikov's compact leaf theorem, every smooth foliation of the 3-sphere includes a compact torus leaf, bounding a solid torus foliated in the same way.
In mathematics, the Reebfoliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1993). It is based...
while the 3-sphere has a famous codimension-1 foliation discovered by Reeb, a codimension-1 foliation of a closed manifold cannot be given by the level...
smaller pieces. In particular, he described what is now called the Reebfoliation, a foliation of the 3-sphere, whose leaves are all diffeomorphic to R 2 {\displaystyle...
foliations are closely related to the concept of Reebless foliation. A taut foliation cannot have a Reeb component, since the component would act like a "dead-end"...
mathematics, Reeb sphere theorem, named after Georges Reeb, states that A closed oriented connected manifold M n that admits a singular foliation having only...
In mathematics, Reeb stability theorem, named after Georges Reeb, asserts that if one leaf of a codimension-one foliation is closed and has finite fundamental...
hyperplane distribution, i.e. that it be tangent to a codimension one foliation on the manifold, whose equivalence is the content of the Frobenius theorem...
1944 Ehresmann inaugurated the theory of foliations, which will be later developed by his student Georges Reeb. With the same perspective, he pioneered...
the category of Reeb graphs is equivalent to a particular class of cosheaf. This is motivated by theoretical work in TDA, since the Reeb graph is related...
Poisson structures the modular class is related to the Reeb class of the underlying symplectic foliation (an element of the first leafwise cohomology group...
Ehresmann-Reeb holonomy or leaf holonomy in reference to the first detailed study using Ehresmann connections to study foliations in (Reeb 1952) See also...
Karcher, Embedded minimal surfaces in the 3-sphere Jürgen Moser, Minimal foliations of tori Edward Witten. Applications of quantum field theory to topology...
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