| dbo: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) 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) |
| dbo:thumbnail |
wiki-commons:Special:FilePath/Immersedsubmanifold_selfintersection.jpg?width=300 |
| dbo:wikiPageID |
525095 (xsd:integer) |
| dbo:wikiPageLength |
7789 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1053098978 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Topological_embedding dbr:Relative_topology dbr:Inclusion_map dbr:Lie_group dbr:Mathematics dbr:Second-countable_space dbr:Closed_map dbr:Alexander's_theorem dbr:Frobenius_theorem_(differential_topology) dbr:Embedding dbr:Wild_arc dbr:Tangent_space dbr:Topology_(structure) dbr:Whitney_embedding_theorem dbr:Linear_subspace dbc:Differential_topology dbc:Manifolds dbr:Foliation dbr:Diffeomorphism dbr:Differential_structure dbr:Graduate_Texts_in_Mathematics dbr:Proper_map dbr:Atlas_(topology) dbr:Differentiability_class dbr:Differentiable_manifold dbr:Manifold dbr:Plane_(mathematics) dbr:Schoenflies_theorem dbr:Open_set dbr:Real_coordinate_space dbr:Neat_submanifold dbr:Chart_(topology) dbr:Image_(mathematics) dbr:Immersion_(mathematics) dbr:Wild_knot dbr:Injective dbr:Subset dbr:Lie_subgroup dbr:Finer_topology dbr:Closed_subset dbr:Compact_set dbr:File:Immersedsubmanifold_nonselfintersection.jpg dbr:File:Immersedsubmanifold_selfintersection.jpg |
| dbp:wikiPageUsesTemplate |
dbt:! dbt:Authority_control dbt:Cite_book dbt:Reflist dbt:Short_description dbt:Manifolds |
| dcterms:subject |
dbc:Differential_topology dbc:Manifolds |
| gold:hypernym |
dbr:S |
| rdf:type |
owl: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: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) |
| rdfs:label |
Untermannigfaltigkeit (de) 部分多様体 (ja) Deelvariëteit (nl) Submanifold (en) Subvariedade (pt) Подмногообразие (ru) 子流形 (zh) Підмноговид (uk) |
| owl:sameAs |
freebase:Submanifold yago-res:Submanifold wikidata:Submanifold dbpedia-de:Submanifold dbpedia-ja:Submanifold dbpedia-nl:Submanifold dbpedia-pt:Submanifold dbpedia-ru:Submanifold dbpedia-uk:Submanifold dbpedia-zh:Submanifold https://global.dbpedia.org/id/HxaH |
| prov:wasDerivedFrom |
wikipedia-en:Submanifold?oldid=1053098978&ns=0 |
| foaf:depiction |
wiki-commons:Special:FilePath/Immersedsubmanifold_nonselfintersection.jpg wiki-commons:Special:FilePath/Immersedsubmanifold_selfintersection.jpg |
| foaf:isPrimaryTopicOf |
wikipedia-en:Submanifold |
| is dbo:wikiPageRedirects of |
dbr:Embedded_submanifold dbr:Slice_chart dbr:Slice_coordinate_system dbr:Regular_submanifold dbr:Immersed_submanifold |
| is dbo:wikiPageWikiLink of |
dbr:Quasi-sphere dbr:Semialgebraic_set dbr:Prime_manifold dbr:De_Sitter_space dbr:Vanya_Mirzoyan dbr:Dupin_hypersurface dbr:Inclusion_map dbr:Induced_metric dbr:Integrability_conditions_for_differential_systems dbr:Lie_groupoid dbr:Transversality_(mathematics) dbr:Weyl's_tube_formula dbr:Maurer–Cartan_form dbr:Chern's_conjecture_for_hypersurfaces_in_spheres dbr:Gauss_map dbr:Geometric_analysis dbr:Geometric_topology dbr:Non-expanding_horizon dbr:Statistical_manifold dbr:Normally_hyperbolic_invariant_manifold dbr:Clifford_torus dbr:Function_of_several_complex_variables dbr:Gerhard_Huisken dbr:Minkowski_space dbr:Osculating_plane dbr:Whitney_disk dbr:Embedding dbr:Harmonic_morphism dbr:Symplectic_manifold dbr:Tangent_space dbr:Maximal_surface dbr:Bang-Yen_Chen dbr:Cauchy_surface dbr:Topological_group dbr:Distribution_(differential_geometry) dbr:G._Peter_Scott dbr:Lebesgue_measure dbr:Linear_flow_on_the_torus dbr:Local_diffeomorphism dbr:Local_flatness dbr:Scott_core_theorem dbr:Stein_manifold dbr:3-manifold dbr:Dynamical_horizon dbr:Ambient_isotopy dbr:Ambient_space dbr:Errett_Bishop dbr:First_class_constraint dbr:Foliation dbr:Non-Euclidean_geometry dbr:Chuu-Lian_Terng dbr:Darboux's_theorem dbr:Darboux_frame dbr:Differential_ideal dbr:Diffiety dbr:Digital_Morse_theory dbr:Foundations_of_Differential_Geometry dbr:Glossary_of_differential_geometry_and_topology dbr:Hilbert_manifold dbr:Isolated_horizon dbr:Isoparametric_manifold dbr:Tangential_and_normal_components dbr:Pseudo-Riemannian_manifold dbr:Riemannian_Penrose_inequality dbr:Riemannian_connection_on_a_surface dbr:Riemannian_manifold dbr:Riemannian_submanifold dbr:2-sided dbr:Inverse_mean_curvature_flow dbr:Terence_Tao dbr:Jenny_Harrison dbr:Projective_differential_geometry dbr:Affine_focal_set dbr:John_Forbes_Nash_Jr. dbr:Laplace–Beltrami_operator dbr:Codimension dbr:Triangulation_(topology) dbr:Tubular_neighborhood dbr:Web_(differential_geometry) dbr:Differentiable_manifold dbr:Manifold dbr:Borel–Moore_homology dbr:Polar_action dbr:Second_fundamental_form dbr:Shing-Tung_Yau dbr:Neat_submanifold dbr:Subanalytic_set dbr:Exterior_calculus_identities dbr:Yoshie_Katsurada dbr:Evolute dbr:First_variation_of_area_formula dbr:Fisher_information_metric dbr:Gibbons–Hawking–York_boundary_term dbr:Whitney_conditions dbr:Topological_quantum_field_theory dbr:Superstring_theory dbr:Taut_submanifold dbr:Embedded_submanifold dbr:Slice_chart dbr:Slice_coordinate_system dbr:Regular_submanifold dbr:Immersed_submanifold |
| is gold:hypernym of |
dbr:Stein_manifold dbr:Isoparametric_manifold dbr:Riemannian_submanifold |
| is foaf:primaryTopic of |
wikipedia-en:Submanifold |
