Search results
Results From The WOW.Com Content Network
2-dimensional section of Reeb foliation 3-dimensional model of Reeb foliation. In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded ...
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 .
The leaf is a torus T 2 bounding a solid torus with the Reeb foliation. The theorem was proved by Sergei Novikov in 1964. Earlier, Charles Ehresmann had conjectured that every smooth codimension-one foliation on S 3 had a compact leaf, which was known to be true for all known examples; in particular, the Reeb foliation has a compact leaf that ...
The distribution/foliation is regular if and only if the action is free. Given a Poisson manifold ( M , π ) {\displaystyle (M,\pi )} , the image of π ♯ = ι π : T ∗ M → T M {\displaystyle \pi ^{\sharp }=\iota _{\pi }:T^{*}M\to TM} is a singular distribution which is always integrable; the leaves of the associated singular foliation are ...
A p-dimensional, class C r foliation of an n-dimensional manifold M is a decomposition of M into a union of disjoint connected submanifolds {L α} α∈A, called the leaves of the foliation, with the following property: Every point in M has a neighborhood U and a system of local, class C r coordinates x=(x 1, ⋅⋅⋅, x n) : U→R n such that ...
A 3-torus in this sense is an example of a 3-dimensional compact manifold. It is also an example of a compact abelian Lie group . This follows from the fact that the unit circle is a compact abelian Lie group (when identified with the unit complex numbers with multiplication).
Well, my last rookie report was on November 7, seven games into the season, when McCain was averaging 6.7 points, 2.0 rebounds, 1.3 assists and 0.4 3s with 46/25/100 shooting splits in just 11 ...
Foliation in geology refers to repetitive layering in metamorphic rocks. [1] Each layer can be as thin as a sheet of paper, or over a meter in thickness. [ 1 ] The word comes from the Latin folium , meaning "leaf", and refers to the sheet-like planar structure. [ 1 ]