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

• Autorzy: Anna Bednarska
• Języki publikacji: EN

Abstrakty

EN

We describe all \(\mathcal{F}^2\mathcal{M}_{m_1,m_2,n_1,n_2}\)-natural operators \(D\colon Q^{\tau}_{proj-proj} \rightsquigarrow QT^*\) transforming projectable-projectable classical torsion-free linear connections \(\nabla\) on fibred-fibred manifolds \(Y\) into classical linear connections \(D(\nabla)\) on cotangent bundles \(T^*Y\) of \(Y\). We show that this problem can be reduced to finding \(\mathcal{F}^2 \mathcal{M}_{m_1,m_2,n_1,n_2}\)-natural operators \(D\colon Q^{\tau}_{proj-proj}\rightsquigarrow(T^*,\otimes^pT^*\otimes\otimes^q T)\) for \(p=2\), \(q=1\) and \(p=3\), \(q=0\).

Słowa kluczowe

EN

Fibred-fibred manifold; projectable-projectable linear connection; natural operator.

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2013
• Tom: 67
• Numer: 1

Daty

wydano

2013

online

2015-07-15

Twórcy

autor

Anna Bednarska

Bibliografia

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• Kurek, J., Mikulski, W. M., The natural liftings of connections to tensor powers of the cotangent bundle, AGMP-8 Proceedings (Brno 2012), Miskolc Mathematical Notes, to appear.
• Kures, M., Natural lifts of classical linear connections to the cotangent bundle, Suppl. Rend. Mat. Palermo II 43 (1996), 181–187.
• Mikulski, W. M., The jet prolongations of fibered-fibered manifolds and the flow operator, Publ. Math. Debrecen 59 (3–4) (2001), 441–458.
• Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York, 1973.

Identyfikatory

DOI

10.17951/a.2013.67.1.1-10