| Title:
|
Higher order jet involution (English) |
| Author:
|
Doupovec, M. |
| Author:
|
Mikulski, W. M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
933-945 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles. (English) |
| Keyword:
|
jet prolongation |
| Keyword:
|
classical linear connection |
| Keyword:
|
higher order connection |
| MSC:
|
58A05 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 1174.58001 |
| idMR:
|
MR2356931 |
| . |
| Date available:
|
2009-09-24T11:50:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128217 |
| . |
| Reference:
|
[1] A. Cabras, I. Kolář: Prolongation of second order connections to vertical Weil bundles.Arch. Math., Brno 37 (2001), 333–347. MR 1879456 |
| Reference:
|
[2] M. Doupovec, I. Kolář: Iteration of fiber product preserving bundle functors.Monatsh. Math. 134 (2001), 39–50. MR 1872045, 10.1007/s006050170010 |
| Reference:
|
[3] M. Doupovec, W. M. Mikulski: On involutions of iterated bundle functors.Colloq. Math 106 (2006), 135–145. MR 2234743, 10.4064/cm106-1-12 |
| Reference:
|
[4] C. Ehresmann: Sur les connexions d’ordre supérieur.Atti del V. Cong. del’Unione Mat. Italiana, 1955, Roma Cremonese (1956), 344–346. |
| Reference:
|
[5] C. Ehresmann: Extension du calcul des jets aux jets non holonomes.C. R. Acad. Sci., Paris 239 (1954), 1762–1764. Zbl 0057.15603, MR 0066734 |
| Reference:
|
[6] I. Kolář, M. Modugno: Natural maps on the iterated jet prolongation of a fibered manifold.Ann. Mat. Pura Appl., IV. Ser. 158 (1991), 151–165. MR 1131848, 10.1007/BF01759302 |
| Reference:
|
[7] I. Kolář: A general point of view to nonholonomic jet bundles.Cah. Topol. Géom. Différ. Catég. 44 (2003), 149–160. MR 1985835 |
| Reference:
|
[8] I. Kolář, P. W. Michor, and J. Slovák: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993. MR 1202431 |
| Reference:
|
[9] I. Kolář, G. Virsik: Connections in first principal prolongations.Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43 (1996), 163–171. MR 1463518 |
| Reference:
|
[10] D. Krupka, J. Janyška: Lectures on Differential Invariants. Folia Facultatis Scientiarum Naturalium Universitatis Purkynianae Brunensis. Mathematica 1.University J. E. Purkyně, Brno, 1990. MR 1108622 |
| Reference:
|
[11] P. Libermann: Introduction to the theory of semi-holonomic jets.Arch. Math. (Brno) 33 (1996), 173–189. Zbl 0915.58004, MR 1478771 |
| Reference:
|
[12] M. Modugno: Jet involution and prolongation of connections.Čas. Pěst. Mat. 114 (1989), 356–365. MR 1027231 |
| Reference:
|
[13] G. Virsik: On the holonomity of higher order connections.Cah. Topol. Géom. Difér. Catég. 12 (1971), 197–212. Zbl 0223.53026, MR 0305294 |
| . |
