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

Anna Bednarska

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 65 (2011), / Harvested from The Polish Digital Mathematics Library

Résumé

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

Détail

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:289785

Bibliographie

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