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- Tangent_bundle abstract "In differential geometry, the tangent bundle of a differentiable manifold M is the disjoint union of the tangent spaces of M. That is,where TxM denotes the tangent space to M at the point x. So, an element of TM can be thought of as a pair (x, v), where x is a point in M and v is a tangent vector to M at x. There is a natural projection defined by π(x, v) = x. This projection maps each tangent space TxM to the single point x.The tangent bundle to a manifold is the prototypical example of a vector bundle (a fiber bundle whose fibers are vector spaces). A section of TM is a vector field on M, and the dual bundle to TM is the cotangent bundle, which is the disjoint union of the cotangent spaces of M. By definition, a manifold M is parallelizable if and only if the tangent bundle is trivial.By definition, a manifold M is framed if and only if the tangent bundle TM is stably trivial, meaning that for some trivial bundle E the Whitney sum TM ⊕ E is trivial. For example, the n-dimensional sphere Sn is framed for all n, but parallelizable only for n=1,3,7 (by results of Bott-Milnor and Kervaire).".
- Tangent_bundle thumbnail Tangent_bundle.svg?width=300.
- Tangent_bundle wikiPageExternalLink AIHPA_1994__61_1_1_0.pdf.
- Tangent_bundle wikiPageExternalLink TangentBundle.html.
- Tangent_bundle wikiPageExternalLink TangentBundle.html.
- Tangent_bundle wikiPageID "211794".
- Tangent_bundle wikiPageRevisionID "600112448".
- Tangent_bundle hasPhotoCollection Tangent_bundle.
- Tangent_bundle id "p/t092110".
- Tangent_bundle title "Tangent bundle".
- Tangent_bundle subject Category:Differential_topology.
- Tangent_bundle subject Category:Vector_bundles.
- Tangent_bundle type Abstraction100002137.
- Tangent_bundle type Collection107951464.
- Tangent_bundle type Group100031264.
- Tangent_bundle type Package108008017.
- Tangent_bundle type VectorBundles.
- Tangent_bundle comment "In differential geometry, the tangent bundle of a differentiable manifold M is the disjoint union of the tangent spaces of M. That is,where TxM denotes the tangent space to M at the point x. So, an element of TM can be thought of as a pair (x, v), where x is a point in M and v is a tangent vector to M at x. There is a natural projection defined by π(x, v) = x.".
- Tangent_bundle label "Fibrado tangente".
- Tangent_bundle label "Fibrado tangente".
- Tangent_bundle label "Fibrato tangente".
- Tangent_bundle label "Fibré tangent".
- Tangent_bundle label "Raakbundel".
- Tangent_bundle label "Tangent bundle".
- Tangent_bundle label "Tangentialbündel".
- Tangent_bundle label "Wiązka styczna".
- Tangent_bundle label "Касательное расслоение".
- Tangent_bundle label "切丛".
- Tangent_bundle sameAs Tangentialbündel.
- Tangent_bundle sameAs Fibrado_tangente.
- Tangent_bundle sameAs Fibré_tangent.
- Tangent_bundle sameAs Fibrato_tangente.
- Tangent_bundle sameAs 접다발.
- Tangent_bundle sameAs Raakbundel.
- Tangent_bundle sameAs Wiązka_styczna.
- Tangent_bundle sameAs Fibrado_tangente.
- Tangent_bundle sameAs m.01f12s.
- Tangent_bundle sameAs Q746550.
- Tangent_bundle sameAs Q746550.
- Tangent_bundle sameAs Tangent_bundle.
- Tangent_bundle wasDerivedFrom Tangent_bundle?oldid=600112448.
- Tangent_bundle depiction Tangent_bundle.svg.
- Tangent_bundle isPrimaryTopicOf Tangent_bundle.