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Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections

100%

Bednarska A.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2011

tom 65

nr 1

We classify all \(\mathcal{F}^2\mathcal{M}_{m_1,m_2,n_1,n_2}\)-natural operators \(A\) transforming projectable-projectable torsion-free classical linear connections \(\nabla\) on fibered-fibered manifolds \(Y\) of dimension \((m_1,m_2, n_1, n_2)\) into \(r\)th order Lagrangians \(A(r)\) on the fibered-fibered linear frame bundle \(L^{fib-fib}(Y )\) on \(Y\). Moreover, we classify all \(\mathcal{F}^2\mathcal{M}_{m_1,m_2,n_1,n_2}\)-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 \(B(\nabla)\) on \(L^{fib-fib}(Y )\). These classifications can be expanded on the \(k\)th order fibered-fibered frame bundle \(L^{fib-fib,k}(Y )\) instead of \(L^{fib-fib}(Y )\).

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1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Bednarska A.

1 2011

Wyniki wyszukiwania

Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections