Higher-order differential equations represented by connections on prolongations of a fibered manifold.

Alexandr Vondra

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Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold.

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Some natural operations between connections on fibred manifolds

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Given a fibered manifold $Y \to X$ , a 2-connection on $Y$ means a section $J^{1} Y \to J^{2} Y$ . The authors determine all first order natural operators transforming a 2-connection on $Y$ and a classical linear connection on $X$ into a connection on $J^{1} Y \to Y$ . (The proof implies that there is no first order natural operator transforming 2-connections on $Y$ into connections on $J^{1} Y \to Y$ .) Using this result, the authors deduce several properties of characterizable connections on $J^{1} Y \to X$ .