Geodesic
Higher order Cartan connections
Archivum mathematicum, Tome 32 (1996) no. 4, pp. 343-354 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 53C05, 58A20
Keywords: non-holonomic jets and connections; semi-holonomic jets and connections; higher order relative; straight and Cartan connections 
@article{ARM_1996_32_4_a8,
     author = {Virsik, George},
     title = {Higher order {Cartan} connections},
     journal = {Archivum mathematicum},
     pages = {343--354},
     year = {1996},
     volume = {32},
     number = {4},
     mrnumber = {1441404},
     zbl = {0881.53014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1996_32_4_a8/}
}
TY  - JOUR
AU  - Virsik, George
TI  - Higher order Cartan connections
JO  - Archivum mathematicum
PY  - 1996
SP  - 343
EP  - 354
VL  - 32
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_1996_32_4_a8/
LA  - en
ID  - ARM_1996_32_4_a8
ER  - 
%0 Journal Article
%A Virsik, George
%T Higher order Cartan connections
%J Archivum mathematicum
%D 1996
%P 343-354
%V 32
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_1996_32_4_a8/
%G en
%F ARM_1996_32_4_a8
Virsik, George. Higher order Cartan connections. Archivum mathematicum, Tome 32 (1996) no. 4, pp. 343-354. http://geodesic.mathdoc.fr/item/ARM_1996_32_4_a8/

[1] Ehresmann C.: Extension du calcul des jets aux jets non holonomes. C.R.A.S. Paris 239(1954), 1762–1764. | MR | Zbl

[2] Ehresmann C.: Sur les connexions d’ordre supérieur. Atti $V^0$ Cong. Un. Mat. Italiana, Pavia-Torino, 1956, 326–328.

[3] Kobayashi S.: Transformation groups in differential geometry. Ergebnisse der Mathematik 70, Springer Verlag, 1972. | MR | Zbl

[4] Kobayashi S., Nomizu K.: Foundations of differential geometry, Vol. 1. Wiley-Interscience, 1963. | MR

[5] Kolář I.: Some higher order operations with connections. Czech. Math. J. 24(99) (1974), 311–330. | MR

[6] Kolář I.: On some operations with connections. Math. Nachrichten 69(1975), 297–306. | MR

[7] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry. Springer-Verlag, 1993. | MR

[8] Virsik G.: Total connections in Lie groupoids. Arch. Math. (Brno) 31 (1995), 183-200. | MR | Zbl

[9] Virsik G.: Bunch connections. Diff. Geom. and Applications, Proc. Conf. 1995, Brno, Czech republic, Masaryk University, Brno (1996), 215-229. | MR | Zbl