On lifts of projectable-projectable classical linear connections to the cotangent bundle

Anna Bednarska

Annales UMCS, Mathematica (2013)

  • Volume: 67, Issue: 1, page 1-10
  • ISSN: 2083-7402

Abstract

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We describe all F2Mm1,m2,n1,n2-natural operators D: Qτproj-prj ↝QT* transforming projectable-projectable classical torsion-free linear connections ∇ on fibred-fibred manifolds Y into classical linear connections D(∇) on cotangent bundles T*Y of Y . We show that this problem can be reduced to finding F2Mm1,m2,n1,n2-natural operators D: Qτproj-proj ↝ (T*,⊗pT*⊗⊗qT) for p = 2, q = 1 and p = 3, q = 0.

How to cite

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Anna Bednarska. "On lifts of projectable-projectable classical linear connections to the cotangent bundle." Annales UMCS, Mathematica 67.1 (2013): 1-10. <http://eudml.org/doc/268229>.

@article{AnnaBednarska2013,
abstract = {We describe all F2Mm1,m2,n1,n2-natural operators D: Qτproj-prj ↝QT* transforming projectable-projectable classical torsion-free linear connections ∇ on fibred-fibred manifolds Y into classical linear connections D(∇) on cotangent bundles T*Y of Y . We show that this problem can be reduced to finding F2Mm1,m2,n1,n2-natural operators D: Qτproj-proj ↝ (T*,⊗pT*⊗⊗qT) for p = 2, q = 1 and p = 3, q = 0.},
author = {Anna Bednarska},
journal = {Annales UMCS, Mathematica},
keywords = {Fibred-fibred manifold; projectable-projectable linear connection; natural operator; fibred-fibred manifold},
language = {eng},
number = {1},
pages = {1-10},
title = {On lifts of projectable-projectable classical linear connections to the cotangent bundle},
url = {http://eudml.org/doc/268229},
volume = {67},
year = {2013},
}

TY - JOUR
AU - Anna Bednarska
TI - On lifts of projectable-projectable classical linear connections to the cotangent bundle
JO - Annales UMCS, Mathematica
PY - 2013
VL - 67
IS - 1
SP - 1
EP - 10
AB - We describe all F2Mm1,m2,n1,n2-natural operators D: Qτproj-prj ↝QT* transforming projectable-projectable classical torsion-free linear connections ∇ on fibred-fibred manifolds Y into classical linear connections D(∇) on cotangent bundles T*Y of Y . We show that this problem can be reduced to finding F2Mm1,m2,n1,n2-natural operators D: Qτproj-proj ↝ (T*,⊗pT*⊗⊗qT) for p = 2, q = 1 and p = 3, q = 0.
LA - eng
KW - Fibred-fibred manifold; projectable-projectable linear connection; natural operator; fibred-fibred manifold
UR - http://eudml.org/doc/268229
ER -

References

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  1. [1] Doupovec, M., Mikulski, W. M., On prolongation of higher order connections, Ann. Polon. Math. 102, no. 3 (2011), 279-292. Zbl1230.58004
  2. [2] Kol´aˇr, I., Connections on fibered squares, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 59 (2005), 67-76. 
  3. [3] Kol´aˇr, I., Michor, P. W., Slov´ak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin-Heidelberg, 1993. 
  4. [4] Kurek, J., Mikulski, W. M., On prolongations of projectable connections, Ann. Polon. Math. 101, no. 3 (2011), 237-250. Zbl1230.58007
  5. [5] Kurek, J., Mikulski, W. M., The natural liftings of connections to tensor powers of thecotangent bundle, AGMP-8 Proceedings (Brno 2012), Miskolc Mathematical Notes, to appear. 
  6. [6] Kur´eˇs, M., Natural lifts of classical linear connections to the cotangent bundle, Suppl. Rend. Mat. Palermo II 43 (1996), 181-187. Zbl0905.53018
  7. [7] Mikulski, W. M., The jet prolongations of fibered-fibered manifolds and the flow operator, Publ. Math. Debrecen 59 (3-4) (2001), 441-458. Zbl0996.58002
  8. [8] Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York, 1973. Zbl0262.53024

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