A Cartan connection associated with a pair $P(M,G^{\prime })\subset P(M,G)$ is defined in the usual manner except that only the injectivity of $\omega :T(P^{\prime })\rightarrow T(G)_{e}$ is required. For an $r$-th order connection associated with a bundle morphism $\Phi :P^{\prime }\rightarrow P$ the concept of Cartan order $q\le r$ is defined, which for $q=r=1, \Phi :P^{\prime }\subset P$, and $\dim {M}=\dim {G/G^{\prime }}$ coincides with the classical definition. Results are obtained concerning the Cartan order of $r$-th order connections that are the product of $r$ first order (Cartan) connections.
@article{107586,
author = {Juraj Virsik},
title = {Higher order Cartan connections},
journal = {Archivum Mathematicum},
volume = {032},
year = {1996},
pages = {343-354},
zbl = {0881.53014},
mrnumber = {1441404},
language = {en},
url = {http://dml.mathdoc.fr/item/107586}
}
Virsik, Juraj. Higher order Cartan connections. Archivum Mathematicum, Tome 032 (1996) pp. 343-354. http://gdmltest.u-ga.fr/item/107586/
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