| Title:
|
Higher order Cartan connections (English) |
| Author:
|
Virsik, George |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
343-354 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
non-holonomic jets and connections |
| Keyword:
|
semi-holonomic jets and connections |
| Keyword:
|
higher order relative |
| Keyword:
|
straight and Cartan connections |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0881.53014 |
| idMR:
|
MR1441404 |
| . |
| Date available:
|
2008-06-06T21:31:48Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107586 |
| . |
| Reference:
|
[1] Ehresmann C.: Extension du calcul des jets aux jets non holonomes.C.R.A.S. Paris 239(1954), 1762–1764. Zbl 0057.15603, MR 0066734 |
| Reference:
|
[2] Ehresmann C.: Sur les connexions d’ordre supérieur.Atti $V^0$ Cong. Un. Mat. Italiana, Pavia-Torino, 1956, 326–328. |
| Reference:
|
[3] Kobayashi S.: Transformation groups in differential geometry.Ergebnisse der Mathematik 70, Springer Verlag, 1972. Zbl 0829.53023, MR 0355886 |
| Reference:
|
[4] Kobayashi S., Nomizu K.: Foundations of differential geometry, Vol. 1.Wiley-Interscience, 1963. MR 0152974 |
| Reference:
|
[5] Kolář I.: Some higher order operations with connections.Czech. Math. J. 24(99) (1974), 311–330. MR 0356114 |
| Reference:
|
[6] Kolář I.: On some operations with connections.Math. Nachrichten 69(1975), 297–306. MR 0391157 |
| Reference:
|
[7] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[8] Virsik G.: Total connections in Lie groupoids.Arch. Math. (Brno) 31 (1995), 183-200. Zbl 0841.53024, MR 1368257 |
| Reference:
|
[9] Virsik G.: Bunch connections.Diff. Geom. and Applications, Proc. Conf. 1995, Brno, Czech republic, Masaryk University, Brno (1996), 215-229. Zbl 0864.53017, MR 1406340 |
| . |
