Geodesic
Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 1.

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We classify all ℱ^2ℳ_m_1,m_2,n_1,n_2-natural operators A transforming projectable-projectable torsion-free classical linear connections ∇ on fibered-fibered manifolds Y of dimension (m_1,m_2, n_1, n_2) into rth order Lagrangians A(r) on the fibered-fibered linear frame bundle L^fib-fib(Y ) on Y. Moreover, we classify all ℱ^2ℳ_m_1,m_2,n_1,n_2-natural operators B transforming projectable-projectable torsion-free classical linear connections r on fiberedfibered manifolds Y of dimension (m_1,m_2, n_1, n_2) into Euler morphism B(∇) on L^fib-fib(Y ). These classifications can be expanded on the kth order fibered-fibered frame bundle L^fib-fib,k(Y ) instead of L^fib-fib(Y ).
Keywords: Fibered-fibered manifold, Lagrangian, Euler morphism, natural operator, classical linear connection 
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Bednarska, Anna. Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 1. http://geodesic.mathdoc.fr/item/AUM_2011_65_1_a4/

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