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

Annales UMCS, Mathematica (2013)

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

## Access Full Article

top## Abstract

top## How to cite

topAnna 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

top- [1] Doupovec, M., Mikulski, W. M., On prolongation of higher order connections, Ann. Polon. Math. 102, no. 3 (2011), 279-292. Zbl1230.58004
- [2] Kol´aˇr, I., Connections on fibered squares, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 59 (2005), 67-76.
- [3] Kol´aˇr, I., Michor, P. W., Slov´ak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin-Heidelberg, 1993.
- [4] Kurek, J., Mikulski, W. M., On prolongations of projectable connections, Ann. Polon. Math. 101, no. 3 (2011), 237-250. Zbl1230.58007
- [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] 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] 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] Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York, 1973. Zbl0262.53024

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.