The contact system for A -jet manifolds

R. J. Alonso-Blanco; J. Muñoz-Díaz

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 3, page 233-248
  • ISSN: 0044-8753

Abstract

top
Jets of a manifold M can be described as ideals of 𝒞 ∞ ( 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.

How to cite

top

Alonso-Blanco, R. J., and Muñoz-Díaz, J.. "The contact system for $A$-jet manifolds." Archivum Mathematicum 040.3 (2004): 233-248. <http://eudml.org/doc/249294>.

@article{Alonso2004,
abstract = {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.},
author = {Alonso-Blanco, R. J., Muñoz-Díaz, J.},
journal = {Archivum Mathematicum},
keywords = {jet; contact system; Weil algebra; Weil bundle; jet; Weil algebra; Weil bundle},
language = {eng},
number = {3},
pages = {233-248},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The contact system for $A$-jet manifolds},
url = {http://eudml.org/doc/249294},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Alonso-Blanco, R. J.
AU - Muñoz-Díaz, J.
TI - The contact system for $A$-jet manifolds
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 3
SP - 233
EP - 248
AB - 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.
LA - eng
KW - jet; contact system; Weil algebra; Weil bundle; jet; Weil algebra; Weil bundle
UR - http://eudml.org/doc/249294
ER -

References

top
  1. Alonso Blanco R. J., Jet manifold associated to a Weil bundle, Arch. Math. (Brno) 36 (2000), 195–199. (199.) MR1785036
  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. MR1978762
  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. (195.) MR1978775
  4. Kolář I., Affine structure on Weil bundles, Nagoya Math. J. 158 (2000), 99–106. Zbl0961.58002MR1766571
  5. Kolář I., Michor P. W., Slovák J., Natural Operations in Differential Geometry, Springer-Verlag, 1993. (1993) MR1202431
  6. Lie S., Theorie der Transformationsgruppen, Leipzig, 1888. (Second edition in Chelsea Publishing Company, New York 1970). (1970) Zbl0248.22009
  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. (1998) MR1708913
  8. Muñoz J., Muriel J., Rodríguez J., Integrability of Lie equations and pseudogroups, J. Math. Anal. Appl. 252 (2000), 32–49. Zbl0973.58008MR1797843
  9. Muñoz J., Muriel J., Rodríguez J., Weil bundles and jet spaces, Czechoslovak Math. J. 50 (125) (2000), no. 4, 721–748. Zbl1079.58500MR1792967
  10. Muñoz J., Muriel J., Rodríguez J., A remark on Goldschmidt’s theorem on formal integrability, J. Math. Anal. Appl. 254 (2001), 275–290. Zbl0999.35003MR1807901
  11. Muñoz J., Muriel J., Rodríguez J., The contact system on the ( m , l ) -jet spaces, Arch. Math. (Brno) 37 (2001), 291–300. MR1879452
  12. Muñoz J., Muriel J., Rodríguez J., On the finiteness of differential invariants, J. Math. Anal. Appl. 284 (2003), No. 1, 266–282. Zbl1070.58005MR1996132
  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. (1990) 
  14. Weil A., Théorie des points proches sur les variétés différentiables, Colloque de Géometrie Différentielle, C. N. R. S. (1953), 111–117. (1953) Zbl0053.24903MR0061455

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.