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In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions.

Attributes	Values
rdf:type	Thing yago:WikicatManifolds yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Tube104493505 yago:Way104564698 yago:Whole100003553
rdfs:label	Untermannigfaltigkeit (de) 部分多様体 (ja) Deelvariëteit (nl) Submanifold (en) Subvariedade (pt) Подмногообразие (ru) 子流形 (zh) Підмноговид (uk)
rdfs:comment	In der Differentialgeometrie beziehungsweise Differentialtopologie ist eine Untermannigfaltigkeit eine Teilmenge einer Mannigfaltigkeit, die mit den Karten der Mannigfaltigkeit verträglich ist. (de) In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions. (en) In de differentiaalmeetkunde, een deelgebied van de wiskunde, is een deelvariëteit van een variëteit M een deelverzameling S, die zelf de structuur van een variëteit heeft, en waarvoor de S → M voldoet aan bepaalde eigenschappen. Er zijn verschillende typen van deelvariëteiten, afhankelijk van precies welke eigenschappen voor een bepaalde toepassing vereist zijn. Verschillende auteurs gebruiken vaak verschillende definities. (nl) 部分多様体（英: submanifold）とは多様体 M の部分集合 S であって、それ自体も多様体構造を持つものを指す。このとき、包含写像 i: S → M の性質によって、部分多様体はいくつかの種類に分けられる。 (ja) Em matemática, a subvariedade de uma variedade M é um subconjunto S que possui ele próprio a estrutura de uma variedade, e para o qual a função inclusão S → M satisfaz certas propriedades. Existem diferentes tipos de subvariedades que dependendo de quais propriedades são exatamente exigidas. Diferentes autores frequentemente tem diferentes definições. (pt) Підмноговид ― термін, що використовується для декількох схожих понять в загальній топології і диференціальній геометрії і алгебричній геометрії. (uk) 数学上，流形M的子流形是子集S，且本身也有流形的结构，并且内含映射S → M满足特定属性。根据具体所需的属性，有各种不同类型的子流形。不同作者经常采用不同的定义。 (zh) Подмногообразие ― термин, используемый для нескольких схожих понятий в общей топологии, дифференциальной геометрии и алгебраической геометрии. (ru)
foaf:depiction
dcterms:subject	Differential topology Manifolds
Wikipage page ID	525095 (xsd:integer)
Wikipage revision ID	1053098978 (xsd:integer)
Link from a Wikipage to another Wikipage	Topological embedding Relative topology Inclusion map Lie group Mathematics Second-countable space Closed map Alexander's theorem Frobenius theorem (differential topology) Embedding Wild arc Tangent space Topology (structure) Whitney embedding theorem Linear subspace Differential topology Manifolds Foliation Diffeomorphism Differential structure Graduate Texts in Mathematics Proper map Atlas (topology) Differentiability class Differentiable manifold Manifold Plane (mathematics) Schoenflies theorem Open set Real coordinate space Neat submanifold Chart (topology) Image (mathematics) Immersion (mathematics) Wild knot Injective Subset Lie subgroup Finer topology Closed subset Compact set
sameAs	Submanifold Submanifold Submanifold Submanifold Submanifold Submanifold Submanifold Submanifold Submanifold Submanifold Submanifold
dbp:wikiPageUsesTemplate	dbt:! dbt:Authority_control dbt:Cite_book dbt:Reflist dbt:Short_description dbt:Manifolds
thumbnail	wiki-commons:Special:FilePath/Immersedsubmanifold_selfintersection.jpg?width=300
has abstract	In der Differentialgeometrie beziehungsweise Differentialtopologie ist eine Untermannigfaltigkeit eine Teilmenge einer Mannigfaltigkeit, die mit den Karten der Mannigfaltigkeit verträglich ist. (de) In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions. (en) In de differentiaalmeetkunde, een deelgebied van de wiskunde, is een deelvariëteit van een variëteit M een deelverzameling S, die zelf de structuur van een variëteit heeft, en waarvoor de S → M voldoet aan bepaalde eigenschappen. Er zijn verschillende typen van deelvariëteiten, afhankelijk van precies welke eigenschappen voor een bepaalde toepassing vereist zijn. Verschillende auteurs gebruiken vaak verschillende definities. (nl)

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