Geodesic
On lifts of projectable-projectable classical linear connections to the cotangent bundle
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 67 (2013) no. 1.

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We describe all ℱ^2ℳ_m_1,m_2,n_1,n_2-natural operators D Q^τ_proj-proj⇝ QT^* transforming projectable-projectable classical torsion-free linear connections ∇ on fibred-fibred manifolds Y into classical linear connections D(∇) on cotangent bundles T^*Y of Y. We show that this problem can be reduced to finding ℱ^2 ℳ_m_1,m_2,n_1,n_2-natural operators D Q^τ_proj-proj⇝(T^*,⊗^pT^*⊗⊗^q T) for p=2, q=1 and p=3, q=0.
Keywords: Fibred-fibred manifold, projectable-projectable linear connection, natural operator. 
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Bednarska, Anna. On lifts of projectable-projectable classical linear connections to the cotangent bundle. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 67 (2013) no. 1. http://geodesic.mathdoc.fr/item/AUM_2013_67_1_a4/

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