The vertical prolongation of the projectable connections

Anna Bednarska

Abstract


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 \(V Y \to M\).

Keywords


Fibred-fibred manifold; natural operator; projectable connection

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References


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DOI: http://dx.doi.org/10.17951/a.2012.66.1.1-5
Data publikacji: 2016-07-24 20:22:23
Data złożenia artykułu: 2016-07-23 09:38:56

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