The vertical prolongation of the projectable connections

• Autorzy: Anna Bednarska
• Języki publikacji: EN

Abstrakty

EN

We prove that any first order \(\mathcal{F}_2\mathcal{M}_{m_1,m_2,n_1,n_2}\)-natural operator transforming projectable general connections on an \((m_1,m_2, n_1, n_2)\)-dimensional fibred-fibred manifold \(p = (p, p) : (p_Y : Y \to Y ) \to (p_M : M \to M)\) into general connections on the vertical prolongation \(V Y \to M\) of \(p: Y \to M\) is the restriction of the (rather well-known) vertical prolongation operator \(\mathcal{V}\) lifting general connections \(\overline{\Gamma}\) on a fibred manifold \(Y \to M\) into \(\mathcal{V}\overline{\Gamma}\) (the vertical prolongation of \(\overline{\Gamma}\)) on \(V Y \to M\).

Słowa kluczowe

EN

Fibred-fibred manifold; natural operator; projectable connection

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2012
• Tom: 66
• Numer: 1

Daty

wydano

2012

online

2016-07-24

Twórcy

autor

Anna Bednarska

Bibliografia

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• Kolar, I., Michor, P. W. and Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
• Kolar, I., Mikulski, W. M., Natural lifting of connections to vertical bundles, The Proceedings of the 19th Winter School “Geometry and Physics” (Srn´ı, 1999). Rend.
• Circ. Mat. Palermo (2) Suppl. No. 63 (2000), 97-102.
• Kurek, J., Mikulski, W. M., On prolongations of projectable connections, Ann. Polon. Math, 101 (2011), no. 3, 237-250.
• Mikulski, W. M., The jet prolongations of fibered-fibered manifolds and the flow operator, Publ. Math. Debrecen 59 (2001), no. 3-4, 441-458.
• Kolar, I., Some natural operations with connections, J. Nat. Acad. Math. India 5 (1987), no. 2, 127-141.

Identyfikatory

DOI

10.17951/a.2012.66.1.1-5