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2. Foliation - Wikipedia

   en.wikipedia.org/wiki/Foliation

   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 ...

3. Frobenius theorem (differential topology) - Wikipedia

   en.wikipedia.org/wiki/Frobenius_theorem...

   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 ...

4. Reeb foliation - Wikipedia

   en.wikipedia.org/wiki/Reeb_foliation

   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 .

5. Hyperbolic 3-manifold - Wikipedia

   en.wikipedia.org/wiki/Hyperbolic_3-manifold

   Hyperbolic geometry is the most rich and least understood of the eight geometries in dimension 3 (for example, for all other geometries it is not hard to give an explicit enumeration of the finite-volume manifolds with this geometry, while this is far from being the case for hyperbolic manifolds).

6. Reeb sphere theorem - Wikipedia

   en.wikipedia.org/wiki/Reeb_sphere_theorem

   A Morse foliation F on a manifold M is a singular transversely oriented codimension one foliation of class with isolated singularities such that: each singularity of F is of Morse type, each singular leaf L contains a unique singularity p ; in addition, if ind ⁡ p = 1 {\displaystyle \operatorname {ind} p=1} then L ∖ p {\displaystyle L ...

7. Cleavage (geology) - Wikipedia

   en.wikipedia.org/wiki/Cleavage_(geology)

   If the heat is too intense, foliation will be weakened due to the nucleation and growth of new randomly oriented crystals and the rock will become a hornfels. [1] If minimal heat is applied to a rock with a preexisting foliation and without a change in mineral assemblage, the cleavage will be strengthened by growth of micas parallel to foliation.