About: Distribution (differential geometry)

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In differential geometry, a discipline within mathematics, a distribution on a manifold is an assignment of vector subspaces satisfying certain properties. In the most common situations, a distribution is asked to be a vector subbundle of the tangent bundle . Distributions satisfying a further integrability condition give rise to foliations, i.e. partitions of the manifold into smaller submanifolds. These notions have several applications in many fields of mathematics, e.g. integrable systems, Poisson geometry, non-commutative geometry, sub-Riemannian geometry, differential topology, etc.

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rdfs:label	Distribuce (diferenciální geometrie) (cs) Distribution (differential geometry) (en) Распределение (дифференциальная геометрия) (ru) Розподіл (диференціальна геометрія) (uk)
rdfs:comment	V diferenciální geometrii se zavádějí jistá zobrazení, která zobrazují z diferencovatelné variety do jejích tečných prostorů. Každému bodu variety je specifickým způsobem přiřazen vektorový prostor, který je podprostorem tečného prostoru v daném bodě variety. Takovýmto zobrazením se říká distribuce. Navzdory svému názvu nemají nic společného s distribucemi alias zobecněnými funkcemi známými z matematické analýzy. (cs) Розподілом на многовиді називається підрозшарування дотичного розшарування многовиду.Іншими словами, у кожній точці вибраний лінійний підпростір дотичного простору що гладко залежить від точки . Розподіли використовуються у теорії інтегровності і в теорії шарувань на многовидах. (uk) Распределением на многообразии называется подрасслоение касательного расслоения многообразия.Другими словами, в каждой точке выбрано линейное подпространство касательного пространства которое гладко зависит от точки . Распределения используются в теории интегрируемости и в теории слоений на многообразии. (ru) In differential geometry, a discipline within mathematics, a distribution on a manifold is an assignment of vector subspaces satisfying certain properties. In the most common situations, a distribution is asked to be a vector subbundle of the tangent bundle . Distributions satisfying a further integrability condition give rise to foliations, i.e. partitions of the manifold into smaller submanifolds. These notions have several applications in many fields of mathematics, e.g. integrable systems, Poisson geometry, non-commutative geometry, sub-Riemannian geometry, differential topology, etc. (en)
differentFrom	Singular distribution
dcterms:subject	Differential geometry Foliations
Wikipage page ID	2976052 (xsd:integer)
Wikipage revision ID	1103902602 (xsd:integer)
Link from a Wikipage to another Wikipage	Vector field Integrable system Integral curve Lie algebroid Lie group Lie group action Differential geometry Mathematics Neighbourhood (mathematics) Tangent bundle Frobenius theorem (differential topology) Block matrices Connected space Control theory Submanifold Lower semicontinuous Chow–Rashevskii theorem Symplectic manifold Foliations G-structure on a manifold Linear combination Linear independence Linear span Foliation Darboux's theorem Differential topology Hamiltonian mechanics Dynamical systems Jet bundle Differentiable manifold Differential geometry Distribution (mathematics) Poisson bracket Orbit (group theory) Lie bracket of vector fields Poisson manifold Subbundle Vector flow Noncommutative geometry Poisson geometry Vector subspace Lie subalgebra Contact structure Sub-Riemannian geometry
Link from a Wikipage to an external page	https://www.uc.pt/fctuc/dmat/seccoes/publicacoes/textosDeMatematica https://link.springer.com/book/10.1007/978-1-4419-9982-5 https://www.ams.org/books/surv/091/ https://www.sciencedirect.com/bookseries/pure-and-applied-mathematics/vol/63/suppl/C
sameAs	Distribution (differential geometry) Distribution (differential geometry) Distribution (differential geometry) Distribution (differential geometry) Distribution (differential geometry) Distribution (differential geometry) Distribution (differential geometry)
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Distinguish dbt:Other_uses dbt:PlanetMath_attribution dbt:Manifolds
id	6541 (xsd:integer) p/i052550 (en)
title	Distribution (en) Involutive distribution (en)
has abstract	V diferenciální geometrii se zavádějí jistá zobrazení, která zobrazují z diferencovatelné variety do jejích tečných prostorů. Každému bodu variety je specifickým způsobem přiřazen vektorový prostor, který je podprostorem tečného prostoru v daném bodě variety. Takovýmto zobrazením se říká distribuce. Navzdory svému názvu nemají nic společného s distribucemi alias zobecněnými funkcemi známými z matematické analýzy. (cs) In differential geometry, a discipline within mathematics, a distribution on a manifold is an assignment of vector subspaces satisfying certain properties. In the most common situations, a distribution is asked to be a vector subbundle of the tangent bundle . Distributions satisfying a further integrability condition give rise to foliations, i.e. partitions of the manifold into smaller submanifolds. These notions have several applications in many fields of mathematics, e.g. integrable systems, Poisson geometry, non-commutative geometry, sub-Riemannian geometry, differential topology, etc. Even though they share the same name, distributions presented in this article have nothing to do with distributions in the sense of analysis. (en) Розподілом на многовиді називається підрозшарування дотичного розшарування многовиду.Іншими словами, у кожній точці вибраний лінійний підпростір дотичного простору що гладко залежить від точки . Розподіли використовуються у теорії інтегровності і в теорії шарувань на многовидах. (uk) Распределением на многообразии называется подрасслоение касательного расслоения многообразия.Другими словами, в каждой точке выбрано линейное подпространство касательного пространства которое гладко зависит от точки . Распределения используются в теории интегрируемости и в теории слоений на многообразии. (ru)
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foaf:isPrimaryTopicOf	wikipedia-en:Distribution_(differential_geometry)
is Link from a Wikipage to another Wikipage of	List of differential geometry topics Almost-contact manifold Gauge theory (mathematics) Frobenius theorem (differential topology) Gheorghe Vrănceanu Contact geometry Singular distribution (differential geometry)

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