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Keywords:
jet; contact system; Weil algebra; Weil bundle
jet; contact system; Weil algebra; Weil bundle
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.
References:
[1] Alonso Blanco R. J.: Jet manifold associated to a Weil bundle. Arch. Math. (Brno) 36 (2000), 195–199. MR 1785036
[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
[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
[4] Kolář I.: Affine structure on Weil bundles. Nagoya Math. J. 158 (2000), 99–106. MR 1766571 | Zbl 0961.58002
[5] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry. Springer-Verlag, 1993. MR 1202431
[6] Lie S.: Theorie der Transformationsgruppen. Leipzig, 1888. (Second edition in Chelsea Publishing Company, New York 1970). Zbl 0248.22009
[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
[8] Muñoz J., Muriel J., Rodríguez J.: Integrability of Lie equations and pseudogroups. J. Math. Anal. Appl. 252 (2000), 32–49. MR 1797843 | Zbl 0973.58008
[9] Muñoz J., Muriel J., Rodríguez J.: Weil bundles and jet spaces. Czechoslovak Math. J. 50 (125) (2000), no. 4, 721–748. MR 1792967 | Zbl 1079.58500
[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 1807901 | Zbl 0999.35003
[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
[12] Muñoz J., Muriel J., Rodríguez J.: On the finiteness of differential invariants. J. Math. Anal. Appl. 284 (2003), No. 1, 266–282. MR 1996132 | Zbl 1070.58005
[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 0061455 | Zbl 0053.24903
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