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

Anna Bednarska

Annales UMCS, Mathematica (2011)

  • Volume: 65, Issue: 1, page 11-19
  • ISSN: 2083-7402

Abstract

top
We classify all F2Mm1, m2, n1, n2-natural operators Atransforming projectable-projectable torsion-free classical linear connections ∇ on fibered-fibered manifolds Y of dimension (m1,m2, n1, n2) into rth order Lagrangians A(∇) on the fibered-fibered linear frame bundle Lfib-fib(Y) on Y. Moreover, we classify all F2Mm1, m2, n1, n2-natural operators B transforming projectable-projectable torsion-free classical linear connections ∇ on fiberedfibered manifolds Y of dimension (m1, m2, n1, n2) into Euler morphism B(∇) on Lfib-fib(Y. These classifications can be expanded on the kth order fibered-fibered frame bundle Lfib-fib,k(Y) instead of Lfib-fib(Y).

How to cite

top

Anna Bednarska. "Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections." Annales UMCS, Mathematica 65.1 (2011): 11-19. <http://eudml.org/doc/268075>.

@article{AnnaBednarska2011,
abstract = {We classify all F2Mm1, m2, n1, n2-natural operators Atransforming projectable-projectable torsion-free classical linear connections ∇ on fibered-fibered manifolds Y of dimension (m1,m2, n1, n2) into rth order Lagrangians A(∇) on the fibered-fibered linear frame bundle Lfib-fib(Y) on Y. Moreover, we classify all F2Mm1, m2, n1, n2-natural operators B transforming projectable-projectable torsion-free classical linear connections ∇ on fiberedfibered manifolds Y of dimension (m1, m2, n1, n2) into Euler morphism B(∇) on Lfib-fib(Y. These classifications can be expanded on the kth order fibered-fibered frame bundle Lfib-fib,k(Y) instead of Lfib-fib(Y).},
author = {Anna Bednarska},
journal = {Annales UMCS, Mathematica},
keywords = {Fibered-fibered manifold; Lagrangian; Euler morphism; natural operator; classical linear connection; fibered-fibered manifold},
language = {eng},
number = {1},
pages = {11-19},
title = {Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections},
url = {http://eudml.org/doc/268075},
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 UMCS, Mathematica
PY - 2011
VL - 65
IS - 1
SP - 11
EP - 19
AB - We classify all F2Mm1, m2, n1, n2-natural operators Atransforming projectable-projectable torsion-free classical linear connections ∇ on fibered-fibered manifolds Y of dimension (m1,m2, n1, n2) into rth order Lagrangians A(∇) on the fibered-fibered linear frame bundle Lfib-fib(Y) on Y. Moreover, we classify all F2Mm1, m2, n1, n2-natural operators B transforming projectable-projectable torsion-free classical linear connections ∇ on fiberedfibered manifolds Y of dimension (m1, m2, n1, n2) into Euler morphism B(∇) on Lfib-fib(Y. These classifications can be expanded on the kth order fibered-fibered frame bundle Lfib-fib,k(Y) instead of Lfib-fib(Y).
LA - eng
KW - Fibered-fibered manifold; Lagrangian; Euler morphism; natural operator; classical linear connection; fibered-fibered manifold
UR - http://eudml.org/doc/268075
ER -

References

top
  1. Kurek, J., Mikulski, W. M., Lagrangians and Euler morphisms from connections on the frame bundle, Proceedings of the XIX International Fall Workshop on Geometry and Physics, Porto, 2010. Zbl1291.53034
  2. Kolář, I., Michor, P. W. and Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. Zbl0782.53013
  3. Kolář, I., Connections on fibered squares, Ann. Univ. Mariae Curie-Skłodowska Sect. A 59 (2005), 67-76. 
  4. Kobayashi, S., Nomizu, K., Foundations of Differential Geometry, Vol. I, Interscience Publisher, New York-London, 1963. Zbl0119.37502
  5. 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. 

NotesEmbed ?

top

You must be logged in to post comments.