Geodesic
The constructions of general connections on second jet prolongation
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 1.

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We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J2Y → M of Y → M. 
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Plaszczyk, Mariusz. The constructions of general connections on second jet prolongation. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 1. http://geodesic.mathdoc.fr/item/AUM_2014_68_1_a4/

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