# Higher order Cartan connections

Archivum Mathematicum (1996)

- Volume: 032, Issue: 4, page 343-354
- ISSN: 0044-8753

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topVirsik, Juraj. "Higher order Cartan connections." Archivum Mathematicum 032.4 (1996): 343-354. <http://eudml.org/doc/18475>.

@article{Virsik1996,

abstract = {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.},

author = {Virsik, Juraj},

journal = {Archivum Mathematicum},

keywords = {non-holonomic jets and connections; semi-holonomic jets and connections; higher order relative; straight and Cartan connections; non-holonomic jets and connections; semi-holonomic jets and connections; higher order derivative; straight and Cartan connections},

language = {eng},

number = {4},

pages = {343-354},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Higher order Cartan connections},

url = {http://eudml.org/doc/18475},

volume = {032},

year = {1996},

}

TY - JOUR

AU - Virsik, Juraj

TI - Higher order Cartan connections

JO - Archivum Mathematicum

PY - 1996

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 032

IS - 4

SP - 343

EP - 354

AB - 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.

LA - eng

KW - non-holonomic jets and connections; semi-holonomic jets and connections; higher order relative; straight and Cartan connections; non-holonomic jets and connections; semi-holonomic jets and connections; higher order derivative; straight and Cartan connections

UR - http://eudml.org/doc/18475

ER -

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- Bunch connections, Diff. Geom. and Applications, Proc. Conf. 1995, Brno, Czech republic, Masaryk University, Brno (1996), 215-229. Zbl0864.53017MR1406340

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