Geodesic
The contact system for $A$-jet manifolds
Archivum mathematicum, Tome 40 (2004) no. 3, pp. 233-248
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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.
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.
Classification : 58A20, 58A32
Keywords: jet; contact system; Weil algebra; Weil bundle 
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Alonso-Blanco, R. J.; Muñoz-Díaz, J. The contact system for $A$-jet manifolds. Archivum mathematicum, Tome 40 (2004) no. 3, pp. 233-248. http://geodesic.mathdoc.fr/item/ARM_2004_40_3_a2/

[1] Alonso Blanco R. J.: Jet manifold associated to a Weil bundle. Arch. Math. (Brno) 36 (2000), 195–199. | MR

[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

[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

[4] Kolář I.: Affine structure on Weil bundles. Nagoya Math. J. 158 (2000), 99–106. | MR | Zbl

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

[6] Lie S.: Theorie der Transformationsgruppen. Leipzig, 1888. (Second edition in Chelsea Publishing Company, New York 1970). | Zbl

[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

[8] Muñoz J., Muriel J., Rodríguez J.: Integrability of Lie equations and pseudogroups. J. Math. Anal. Appl. 252 (2000), 32–49. | MR | Zbl

[9] Muñoz J., Muriel J., Rodríguez J.: Weil bundles and jet spaces. Czechoslovak Math. J. 50 (125) (2000), no. 4, 721–748. | MR | Zbl

[10] Muñoz J., Muriel J., Rodríguez J.: A remark on Goldschmidt’s theorem on formal integrability. J. Math. Anal. Appl. 254 (2001), 275–290. | MR | Zbl

[11] Muñoz J., Muriel J., Rodríguez J.: The contact system on the $(m,l)$-jet spaces. Arch. Math. (Brno) 37 (2001), 291–300. | MR

[12] Muñoz J., Muriel J., Rodríguez J.: On the finiteness of differential invariants. J. Math. Anal. Appl. 284 (2003), No. 1, 266–282. | MR | Zbl

[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.

[14] Weil A.: Théorie des points proches sur les variétés différentiables. Colloque de Géometrie Différentielle, C. N. R. S. (1953), 111–117. | MR | Zbl