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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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