Talk:Jet (mathematics)

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[edit] Jet bundles and jets

The definition in Jet bundles does not agree with the definition I am familiar with. There are various definitions in the literature, depending on the context. If anyone happens to be familiar with the original Ehresmann paper, please check it out:

• Ehresmann, C., "Introduction a la théorie des structures infinitésimales et des pseudo-groupes de Lie." Geometrie Differentielle, Colloq. Inter. du Centre Nat. de la Recherche Scientifique, Strasbourg, 1953, 97-127.

In short, iterated jet spaces are not the same as jet spaces. There are various types of holonomic constraints that people impose on iterated jets; for instance holonomic (pure) jets, semi-holonomic jets, and non-holonomic jets. In any case, (pure) jets are fundamental for distinguishing between these cases.151.204.6.171

The higher order tangent bundles T^kM with k > 1 are not vector bundles. The transition functions are certainly non-singular, but for a vector bundle you also need them to be linear in the fibre cdoordinates.83.104.131.53 12:44, 5 February 2006 (UTC)