: Matemáticas: foliation

geometry > differential geometry > foliation

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 Rⁿ into the cosets x + R^p of the standardly embedded subspace R^p. The equivalence classes are called the leaves of the foliation. If the manifold and/or the submanifolds are required to have a piecewise-linear, differentiable (of class C^r), or analytic structure then one defines piecewise-linear, differentiable, or analytic foliations, respectively. In the most important case of differentiable foliation of class C^r it is usually understood that r ≥ 1 (otherwise, C⁰ is a topological foliation). The number p (the dimension of the leaves) is called the dimension of the foliation and q = n − p is called its codimension.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Foliation)

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