High Quality Content by WIKIPEDIA articles! In differential geometry, the jet bundle is a certain construction which makes a new smooth fiber bundle out of a given smooth fiber bundle. It makes it possible to write differential equations on sections of a fiber bundle in an invariant form. Historically, jet bundles are attributed to Ehresmann, and were an advance on the method (prolongation) of Elie Cartan, of dealing geometrically with higher derivatives, by imposing differential form conditions on newly-introduced formal variables. Jet bundles are sometimes called sprays, although sprays usually refer more specifically to the associated vector field induced on the corresponding bundle (e.g., the geodesic spray on Finsler manifolds.)

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