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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, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane (a tangent plane) to a small and close enough observer, all 3-manifolds look like our universe does to a small enough observer ...
In geotechnical engineering, a foliation plane may introduce anisotropy of stress, which is a vital consideration for geotechnical engineers. At some point, this foliation may form a discontinuity that may greatly influence the mechanical behavior (strength, deformation, etc.) of rock masses in, for example, tunnel, foundation, or slope ...
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.
In other words, every point admits a foliation chart, i.e. the distribution is tangent to the leaves of a foliation. Moreover, this local characterisation coincides with the definition of integrability for a G {\displaystyle G} -structures , when G {\displaystyle G} is the group of real invertible upper-triangular block matrices (with ( n × n ...
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 ...
[3] Crystallographic preferred orientation — in plastically deformed rocks, the constituent minerals commonly display a preferred orientation of their crystal axes as a result of dislocation processes. S-fabric — a planar fabric such as cleavage or foliation; when it forms the dominant fabric in a rock, it may be called an S-tectonite.
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.