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- Parallel_transport abstract "In geometry, parallel transport is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection allows one to transport vectors of the manifold along curves so that they stay parallel with respect to the connection. Other notions of connection come equipped with their own parallel transportation systems as well. For instance, a Koszul connection in a vector bundle also allows for the parallel transport of vectors in much the same way as with a covariant derivative. An Ehresmann or Cartan connection supplies a lifting of curves from the manifold to the total space of a principal bundle. Such curve lifting may sometimes be thought of as the parallel transport of reference frames.The parallel transport for a connection thus supplies a way of, in some sense, moving the local geometry of a manifold along a curve: that is, of connecting the geometries of nearby points. There may be many notions of parallel transport available, but a specification of one — one way of connecting up the geometries of points on a curve — is tantamount to providing a connection. In fact, the usual notion of connection is the infinitesimal analog of parallel transport. Or, vice versa, parallel transport is the local realization of a connection. As parallel transport supplies a local realization of the connection, it also supplies a local realization of the curvature known as holonomy. The Ambrose-Singer theorem makes explicit this relationship between curvature and holonomy.".
- Parallel_transport thumbnail Parallel_transport.png?width=300.
- Parallel_transport wikiPageExternalLink dragsphere.
- Parallel_transport wikiPageID "285595".
- Parallel_transport wikiPageRevisionID "574405866".
- Parallel_transport first "Ü.".
- Parallel_transport hasPhotoCollection Parallel_transport.
- Parallel_transport id "c/c025180".
- Parallel_transport last "Lumiste".
- Parallel_transport title "Connections on a manifold".
- Parallel_transport year "2001".
- Parallel_transport subject Category:Connection_(mathematics).
- Parallel_transport subject Category:Riemannian_geometry.
- Parallel_transport comment "In geometry, parallel transport is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection allows one to transport vectors of the manifold along curves so that they stay parallel with respect to the connection. Other notions of connection come equipped with their own parallel transportation systems as well.".
- Parallel_transport label "Parallel transport".
- Parallel_transport label "Parallel transport".
- Parallel_transport label "Paralleltransport".
- Parallel_transport label "Przeniesienie równoległe".
- Parallel_transport label "Transporte paralelo".
- Parallel_transport label "Transporte paralelo".
- Parallel_transport label "Параллельное перенесение".
- Parallel_transport label "平行移动".
- Parallel_transport sameAs Paralleltransport.
- Parallel_transport sameAs Transporte_paralelo.
- Parallel_transport sameAs Parallel_transport.
- Parallel_transport sameAs Przeniesienie_równoległe.
- Parallel_transport sameAs Transporte_paralelo.
- Parallel_transport sameAs m.01pzm2.
- Parallel_transport sameAs Q1814838.
- Parallel_transport sameAs Q1814838.
- Parallel_transport wasDerivedFrom Parallel_transport?oldid=574405866.
- Parallel_transport depiction Parallel_transport.png.
- Parallel_transport isPrimaryTopicOf Parallel_transport.
