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

Anna Bednarska. "Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 65.1 (2011): null. <http://eudml.org/doc/289785>.

@article{AnnaBednarska2011,
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 $L^\{fib-fib\}(Y )$.},
author = {Anna Bednarska},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Fibered-fibered manifold; Lagrangian; Euler morphism; natural operator; classical linear connection},
language = {eng},
number = {1},
pages = {null},
title = {Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections},
url = {http://eudml.org/doc/289785},
volume = {65},
year = {2011},
}

TY - JOUR
AU - Anna Bednarska
TI - Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2011
VL - 65
IS - 1
SP - null
AB - 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 $L^{fib-fib}(Y )$.
LA - eng
KW - Fibered-fibered manifold; Lagrangian; Euler morphism; natural operator; classical linear connection
UR - http://eudml.org/doc/289785
ER -