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

Anna Bednarska

Abstract


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 \(L^{fib-fib}(Y )\).

Keywords


Fibered-fibered manifold; Lagrangian; Euler morphism; natural operator; classical linear connection

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References


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Kurek, J., Mikulski, W. M., On the formal Euler operator from the variational calculus in fibered-fibered manifolds, Proc. of the 6 International Conference Aplimat 2007, Bratislava, 223-229.




DOI: http://dx.doi.org/10.17951/a.2011.65.1.11-19
Data publikacji: 2016-07-25 18:17:30
Data złożenia artykułu: 2016-07-25 15:07:38

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Copyright (c) 2011 Anna Bednarska