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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 .
Intersection lineations are linear structures formed by the intersection of any two surfaces in a three-dimensional space. The trace of bedding on an intersecting foliation plane commonly appears as colour stripes generally parallel to local fold's hinges. Intersection lineations can also be due to the intersection of two foliations.
Generally, these structures are formed in fine grained rocks composed of minerals affected by pressure solution. [1] Cleavage is a type of rock foliation, a fabric element that describes the way planar features develop in a rock. Foliation is separated into two groups: primary and secondary.
The distribution/foliation is regular If and only if the Poisson manifold is regular. More generally, the image of the anchor map ρ : A → T M {\displaystyle \rho :A\to TM} of any Lie algebroid A → M {\displaystyle A\to M} defines a singular distribution which is automatically integrable, and the leaves of the associated singular foliation ...
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 ...