Geodesic
The vertical prolongation of the projectable connections
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 66 (2012) no. 1.

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We prove that any first order ℱ_2ℳ_m_1,m_2,n_1,n_2-natural operator transforming projectable general connections on an (m_1,m_2, n_1, n_2)-dimensional fibred-fibred manifold p = (p, p) : (p_Y : Y → Y ) → (p_M : M → M) into general connections on the vertical prolongation V Y → M of p: Y → M is the restriction of the (rather well-known) vertical prolongation operator 𝒱 lifting general connections Γ on a fibred manifold Y → M into 𝒱Γ (the vertical prolongation of Γ) on V Y → M.
Keywords: Fibred-fibred manifold, natural operator, projectable connection 
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Bednarska, Anna. The vertical prolongation of the projectable connections. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 66 (2012) no. 1. http://geodesic.mathdoc.fr/item/AUM_2012_66_1_a7/

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