| Title:
|
On the iterated absolute differentiation on some functional bundles (English) |
| Author:
|
Cabras, Antonella |
| Author:
|
Kolář, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
23-35 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deduce further properties of connections on the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base, which we introduced in [2]. In particular, we define the vertical prolongation of such a connection, discuss the iterated absolute differentiation by means of an auxiliary linear connection on the base manifold and prove the general Ricci identity. (English) |
| Keyword:
|
bundle of smooth maps |
| Keyword:
|
connection on a functional bundle |
| Keyword:
|
iterated absolute differentiation |
| Keyword:
|
iterated 2-jet |
| Keyword:
|
Ricci identity |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0910.53014 |
| idMR:
|
MR1464298 |
| . |
| Date available:
|
2008-06-06T21:32:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107594 |
| . |
| Reference:
|
[1] Cabras A.: The Ricci identity for general connections.Proceedings Conf. Diff. Geom. and Applications, 1995, Masaryk University, Brno 1996, 121-126. Zbl 0862.53023, MR 1406331 |
| Reference:
|
[2] Cabras A., Kolář I.: Connections on some functional bundles.Czechoslovak Math. J., 45(1995), 529-548. MR 1344519 |
| Reference:
|
[3] Cabras A., Kolář I.: The universal connection of an arbitrary system.to appear in Annali di Matematica. MR 1746921 |
| Reference:
|
[4] Ehresmann C.: Extension du calcul des jets aux jets non holonomes.CRAS Paris, 239 (1954), 1762-1764. Zbl 0057.15603, MR 0066734 |
| Reference:
|
[5] Frölicher A.: Smooth structures.Category theory 1981, LNM 962, Springer-Verlag, 1982, 69-81. MR 0682945 |
| Reference:
|
[6] Jadczyk A., Modugno M.: Galilei general relativistic quantum mechanics.to appear. |
| Reference:
|
[7] Kolář I.: Connections in 2-fibred manifolds.Arch. Math.(Brno), XVII(1981), 23-30. MR 0672485 |
| Reference:
|
[8] Kolář I: Higher order absolute differentiation with respect to generalized connections.Differential Geometry, Banach Center Publications, Volume 12, Warszaw 1984, 153-162. MR 0961078 |
| Reference:
|
[9] Kolář I.: An infinite dimensional motivation in higher order geometry.Proceedings Conf. Diff. Geom. and Applications, 1995, Masaryk University, Brno 1996, 151-159. MR 1406335 |
| Reference:
|
[10] Kolář I., Michor P. W., Slovák J.: Natural operations in differential geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[11] Mangiarotti L., Modugno M.: Connections and differential calculus on fibered manifolds.preprint. |
| Reference:
|
[12] Modugno M.: New results on the theory of connections: systems, overconnections and prolongations.Differential Geometry and Its Applications, Proceedings, D. Reidel Publishing Company, 1987, 243-269. Zbl 0636.53039, MR 0923352 |
| Reference:
|
[13] Pradines J.: Représentation des jets non holonomes par des morphisms vectoriels doubles soudés.CRAS Paris, série A 278, 1974, 1523-1526. MR 0388432 |
| Reference:
|
[14] Slovák J.: Smooth structures on fibre jet spaces.Czechoslovak Math. J., 36(1986), 358-375. MR 0847766 |
| Reference:
|
[15] Virsik G.: Total connections in Lie groupoids.Arch. Math.(Brno), 31(1995), 183-200. Zbl 0841.53024, MR 1368257 |
| . |
