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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