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
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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
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- [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
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