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In mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered bases, or frames, for Ex. The general linear group acts naturally on F(E) via a change of basis, giving the frame bundle the structure of a principal GL(k, R)-bundle (where k is the rank of E). The frame bundle of a smooth manifold is the one associated to its tangent bundle. For this reason it is sometimes called the tangent frame bundle.

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rdf:type	Thing yago:WikicatVectorBundles yago:Abstraction100002137 yago:Collection107951464 yago:Group100031264 yago:Package108008017 motorsport season
rdfs:label	Fibrat de marc (ca) Rahmenbündel (de) Fibré des repères (fr) Frame bundle (en) 틀다발 (ko) Розшарування реперів (uk) 标架丛 (zh)
rdfs:comment	In mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered bases, or frames, for Ex. The general linear group acts naturally on F(E) via a change of basis, giving the frame bundle the structure of a principal GL(k, R)-bundle (where k is the rank of E). The frame bundle of a smooth manifold is the one associated to its tangent bundle. For this reason it is sometimes called the tangent frame bundle. (en) 위상수학에서 틀다발(영어: frame bundle)은 임의의 벡터 다발에 대응되는, 일반 선형군을 올로 삼는 특별한 주다발이다.:§4.3, 121–131 벡터 다발의 틀다발은 원래 벡터 다발의 위상수학적 정보를 담고 있으며, 원래 벡터 다발은 틀다발의 연관 벡터 다발로서 재구성된다. (ko) У математиці, розшаруванням реперів називається головне розшарування F(E) асоційоване із деяким векторним розшаруванням E. Шаром над точкою x у F(E) є множина всіх впорядкованих базисів, або реперів векторного простору Ex. Загальна лінійна група натурально діє на F(E) заміною базисів. Із цією дією розшарування реперів є головним GL(k, R)-розшаруванням (де k є рангом E). Для гладкого многовиду розшарування реперів розглядають в основному для дотичного розшарування. Воно також називається дотичним розшаруванням реперів. (uk) 数学中，标架丛（Frame bundle）是一个与任何向量丛 E 相伴的主丛。F(E) 在一点 x 的纤维是 Ex 的所有有序基或曰标架。一般线性群通过基变更自然作用在 F(E) 上，给出标架丛一个主 GLk(R)-丛结构，这里 k 是 E 的秩。一个光滑流形的标架丛是与其切丛相伴的丛。因此它有经常称为切标架丛（tangent frame bundle）。 (zh) In der Mathematik im Teilgebiet der Differentialgeometrie ist ein Rahmenbündel ein Hauptfaserbündel, das zu einem Vektorbündel zugeordnet ist. Grob gesagt entspricht das Rahmenbündel der Menge aller Basen des zugeordneten Vektorbündeln. Die Elemente eines Rahmenbündels werden als Rahmen bezeichnet. Von besonderem Interesse ist das Rahmenbündel, das dem Tangentialbündel einer glatten Mannigfaltigkeit zugeordnet wird. (de) En géométrie différentielle, un fibré des repères est un certain type de fibré principal qui correspond à un fibré vectoriel sur une variété différentielle. Les points du fibré des repères sont les repères linéaires des fibres du fibré vectoriel correspondant. (fr)
rdfs:seeAlso	G-structure
foaf:depiction
dcterms:subject	Vector bundles Fiber bundles
Wikipage page ID	366550 (xsd:integer)
Wikipage revision ID	1068157656 (xsd:integer)
Link from a Wikipage to another Wikipage	Pushforward (differential) Vector-valued differential form Euclidean metric Almost complex manifold Homeomorphic Volume form Mathematics General linear group Tangent bundle Function composition Linear isomorphism Complex manifold Orthonormal basis G-structure Calabi–Yau manifold Vector bundles Torsor Undefined (mathematics) Dual bundle Dual representation Equivalence relation Foundations of Differential Geometry Equivariant Free action Orthonormal frame Riemannian bundle metric Riemannian manifold Group action (mathematics) Fiber bundles Change of basis Tautological one-form Disjoint union Associated bundle Bundle map Fiber bundle construction theorem Final topology Method of moving frames Identity function Inner product space Orbit (group theory) Orientability Orthogonal group Reduction of the structure group Section (fiber bundle) Smooth manifold Vector bundle Linear isometry Tensorial form Subbundle Nondegenerate form Space (mathematics) Solder form Parallelizable manifold Lie subgroup Tensor bundle Linear representation Transition map Transitive action Ordered basis 2-form Naturally isomorphic Wiley Interscience Principal fiber bundle Smooth frame Integrability condition Closed differential form Local trivialization Structure group
Link from a Wikipage to an external page	https://web.archive.org/web/20170330154524/http:/www.emis.de/monographs/KSM/kmsbookh.pdf%7Carchive-date=2017-03-30%7Curl-status=dead http://www.emis.de/monographs/KSM/kmsbookh.pdf%7Cformat=PDF%7Ctitle=Natural
sameAs	Frame bundle Frame bundle Frame bundle

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