What does foliation mean?

Definitions for foliation
ˌfoʊ liˈeɪ ʃənfo·li·a·tion

This dictionary definitions page includes all the possible meanings, example usage and translations of the word foliation.

Princeton's WordNet

  1. foliation, leafingnoun

    (botany) the process of forming leaves

  2. foliationnoun

    (geology) the arrangement of leaflike layers in a rock

  3. foliation, foliagenoun

    (architecture) leaf-like architectural ornament

  4. foliationnoun

    the production of foil by cutting or beating metal into thin leaves

  5. foliationnoun

    the work of coating glass with metal foil

Wiktionary

  1. foliationnoun

    The process of forming into a leaf or leaves.

  2. foliationnoun

    The manner in which the young leaves are disposed within the bud.

  3. foliationnoun

    The act of beating a metal into a thin plate, leaf, foil, or lamina.

  4. foliationnoun

    The act of coating with an amalgam of tin foil and quicksilver, as in making looking-glasses.

  5. foliationnoun

    The enrichment of an opening by means of foils, arranged in trefoils, quatrefoils, etc.; also, one of the ornaments.

  6. foliationnoun

    The property, possessed by some crystalline rocks, of dividing into plates or slabs, which is due to the cleavage structure of one of the constituents, as mica or hornblende. It may sometimes include slaty structure or cleavage, though the latter is usually independent of any mineral constituent, and transverse to the bedding, it having been produced by pressure.

  7. foliationnoun

    A set of submanifolds of a given manifold, each of which is of lower dimension than it, but which, taken together, are coextensive with it.

Samuel Johnson's Dictionary

  1. Foliationnoun

    Etymology: foliatio, folium, Latin.

Wikipedia

  1. 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 + Rp of the standardly embedded subspace Rp. 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 Cr), or analytic structure then one defines piecewise-linear, differentiable, or analytic foliations, respectively. In the most important case of differentiable foliation of class Cr 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. In some papers on general relativity by mathematical physicists, the term foliation (or slicing) is used to describe a situation where the relevant Lorentz manifold (a (p+1)-dimensional spacetime) has been decomposed into hypersurfaces of dimension p, specified as the level sets of a real-valued smooth function (scalar field) whose gradient is everywhere non-zero; this smooth function is moreover usually assumed to be a time function, meaning that its gradient is everywhere time-like, so that its level-sets are all space-like hypersurfaces. In deference to standard mathematical terminology, these hypersurface are often called the leaves (or sometimes slices) of the foliation. Note that while this situation does constitute a codimension-1 foliation in the standard mathematical sense, examples of this type are actually globally trivial; while the leaves of a (mathematical) codimension-1 foliation are always locally the level sets of a function, they generally cannot be expressed this way globally, as a leaf may pass through a local-trivializing chart infinitely many times, and the holonomy around a leaf may also obstruct the existence of a globally-consistent defining functions for the leaves. For example, while the 3-sphere has a famous codimension-1 foliation discovered by Reeb, a codimension-1 foliation of a closed manifold cannot be given by the level sets of a smooth function, since a smooth function on a closed manifold necessarily has critical points at its maxima and minima.

ChatGPT

  1. foliation

    Foliation in geology refers to the repetitive layering or banding in metamorphic rocks. Each layer or band can be as thin as a sheet of paper, or thicker than a meter. This property can occur as a result of various geological processes like deformation or crystallization. The term "foliation" is derived from the Latin word "folium" which means leaf, indicating the leaf-like appearance of the layers in foliated rocks. While in mathematics, particularly in differential geometry and topology, foliation is a partition of a topological space into disjoint, connected, and often similar parts, referred to as leaves. Each leaf in this abstract structure is usually a submanifold of the topological space. In the field of botany, foliation refers to the arrangement of leaves on a stem or the process of forming leaves. In general, foliation represents the concept of layered structure or process across several fields.

Webster Dictionary

  1. Foliationnoun

    the process of forming into a leaf or leaves

  2. Foliationnoun

    the manner in which the young leaves are dispo/ed within the bud

  3. Foliationnoun

    the act of beating a metal into a thin plate, leaf, foil, or lamina

  4. Foliationnoun

    the act of coating with an amalgam of tin foil and quicksilver, as in making looking-glasses

  5. Foliationnoun

    the enrichment of an opening by means of foils, arranged in trefoils, quatrefoils, etc.; also, one of the ornaments. See Tracery

  6. Foliationnoun

    the property, possessed by some crystalline rocks, of dividing into plates or slabs, which is due to the cleavage structure of one of the constituents, as mica or hornblende. It may sometimes include slaty structure or cleavage, though the latter is usually independent of any mineral constituent, and transverse to the bedding, it having been produced by pressure

  7. Etymology: [Cf. F. foliation.]

Wikidata

  1. Foliation

    In mathematics, a foliation is a geometric device used to study manifolds, consisting of an integrable subbundle of the tangent bundle. A foliation looks locally like a decomposition of the manifold as a union of parallel submanifolds of smaller dimension.

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Numerology

  1. Chaldean Numerology

    The numerical value of foliation in Chaldean Numerology is: 1

  2. Pythagorean Numerology

    The numerical value of foliation in Pythagorean Numerology is: 2

Popularity rank by frequency of use

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"foliation." Definitions.net. STANDS4 LLC, 2024. Web. 21 May 2024. <https://www.definitions.net/definition/foliation>.

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