| Title:
|
The contact system for $A$-jet manifolds (English) |
| Author:
|
Alonso-Blanco, R. J. |
| Author:
|
Muñoz-Díaz, J. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
233-248 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Jets of a manifold $M$ can be described as ideals of $\mathcal {C}^\infty (M)$. This way, all the usual processes on jets can be directly referred to that ring. By using this fact, we give a very simple construction of the contact system on jet spaces. The same way, we also define the contact system for the recently considered $A$-jet spaces, where $A$ is a Weil algebra. We will need to introduce the concept of derived algebra. (English) |
| Keyword:
|
jet |
| Keyword:
|
contact system |
| Keyword:
|
Weil algebra |
| Keyword:
|
Weil bundle |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1112.58002 |
| idMR:
|
MR2107018 |
| . |
| Date available:
|
2008-06-06T22:43:43Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107906 |
| . |
| Reference:
|
[1] Alonso Blanco R. J.: Jet manifold associated to a Weil bundle.Arch. Math. (Brno) 36 (2000), 195–199. MR 1785036 |
| Reference:
|
[2] Alonso Blanco R. J.: On the local structure of $A$-jet manifolds.In: Proceedings of Diff. Geom. and its Appl. (Opava, 2002), Math Publ. 3, Silesian Univ. Opava 2001, 51–61. MR 1978762 |
| Reference:
|
[3] Jiménez S., Muñoz J., Rodríguez J.: On the reduction of some systems of partial differential equations to first order systems with only one unknown function.In: Proceedings of Diff. Geom. and its Appl. (Opava, 2002), Math. Publ. 3, Silesian Univ. Opava 2001, 187–195. MR 1978775 |
| Reference:
|
[4] Kolář I.: Affine structure on Weil bundles.Nagoya Math. J. 158 (2000), 99–106. Zbl 0961.58002, MR 1766571 |
| Reference:
|
[5] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[6] Lie S.: Theorie der Transformationsgruppen.Leipzig, 1888. (Second edition in Chelsea Publishing Company, New York 1970). Zbl 0248.22009 |
| Reference:
|
[7] Muñoz J., Muriel J., Rodríguez J.: The canonical isomorphism between the prolongation of the symbols of a nonlinear Lie equation and its attached linear Lie equation.in Proccedings of Diff. Geom. and its Appl. (Brno, 1998), Masaryk Univ., Brno 1999, 255–261. MR 1708913 |
| Reference:
|
[8] Muñoz J., Muriel J., Rodríguez J.: Integrability of Lie equations and pseudogroups.J. Math. Anal. Appl. 252 (2000), 32–49. Zbl 0973.58008, MR 1797843 |
| Reference:
|
[9] Muñoz J., Muriel J., Rodríguez J.: Weil bundles and jet spaces.Czechoslovak Math. J. 50 (125) (2000), no. 4, 721–748. Zbl 1079.58500, MR 1792967 |
| Reference:
|
[10] Muñoz J., Muriel J., Rodríguez J.: A remark on Goldschmidt’s theorem on formal integrability.J. Math. Anal. Appl. 254 (2001), 275–290. Zbl 0999.35003, MR 1807901 |
| Reference:
|
[11] Muñoz J., Muriel J., Rodríguez J.: The contact system on the $(m,l)$-jet spaces.Arch. Math. (Brno) 37 (2001), 291–300. MR 1879452 |
| Reference:
|
[12] Muñoz J., Muriel J., Rodríguez J.: On the finiteness of differential invariants.J. Math. Anal. Appl. 284 (2003), No. 1, 266–282. Zbl 1070.58005, MR 1996132 |
| Reference:
|
[13] Rodríguez J.: Sobre los espacios de jets y los fundamentos de la teoría de los sistemas de ecuaciones en derivadas parciales.Ph. D. Thesis, Salamanca, 1990. |
| Reference:
|
[14] Weil A.: Théorie des points proches sur les variétés différentiables.Colloque de Géometrie Différentielle, C. N. R. S. (1953), 111–117. Zbl 0053.24903, MR 0061455 |
| . |
