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Higher order Cartan connections. (English) Zbl 0881.53014
Let \(P(M,G)\), \(p:P\to M\), be a principal bundle and \(P'(M,G')\subset P(M,G)\) be its reduction. For a morphism \((\Phi ,\Phi _G):P'(M,G')\to P(M,G)\) an \(r\)-th order \(\Phi \)-connection is defined to be a morphism \(\Gamma :P'\to \tilde J^rP\) which satisfies \(\pi ^r_0\circ \Gamma =\Phi \) and \(\Gamma (h'g')=\Gamma (h')\cdot j^r_{p'h'}[\Phi _G(g')]\), where \(\tilde J^rP\) is the fibred manifold of non-holonomic jets of sections and \(g'\in G'\). The concept of Cartan order \(q\leq r\) for a \(\Phi \)-connection is defined. Cartan orders of \(\Phi \)-connections arising from first order (Cartan) connections on \(P'\) and \(P\) are studied.
Reviewer: J.Janyška (Brno)
MSC:
53C05 Connections, general theory
58A20 Jets in global analysis
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