Higher order jet involution

Miroslav Doupovec; Włodzimierz M. Mikulski

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 3, page 933-945
  • ISSN: 0011-4642

Abstract

top
We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.

How to cite

top

Doupovec, Miroslav, and Mikulski, Włodzimierz M.. "Higher order jet involution." Czechoslovak Mathematical Journal 57.3 (2007): 933-945. <http://eudml.org/doc/31173>.

@article{Doupovec2007,
abstract = {We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.},
author = {Doupovec, Miroslav, Mikulski, Włodzimierz M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {jet prolongation; classical linear connection; higher order connection; jet prolongation; classical linear connection; higher order connection},
language = {eng},
number = {3},
pages = {933-945},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Higher order jet involution},
url = {http://eudml.org/doc/31173},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Doupovec, Miroslav
AU - Mikulski, Włodzimierz M.
TI - Higher order jet involution
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 933
EP - 945
AB - We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.
LA - eng
KW - jet prolongation; classical linear connection; higher order connection; jet prolongation; classical linear connection; higher order connection
UR - http://eudml.org/doc/31173
ER -

References

top
  1. Prolongation of second order connections to vertical Weil bundles, Arch. Math., Brno 37 (2001), 333–347. (2001) MR1879456
  2. 10.1007/s006050170010, Monatsh. Math. 134 (2001), 39–50. (2001) MR1872045DOI10.1007/s006050170010
  3. 10.4064/cm106-1-12, Colloq. Math 106 (2006), 135–145. (2006) MR2234743DOI10.4064/cm106-1-12
  4. Sur les connexions d’ordre supérieur, Atti del V.  Cong. del’Unione Mat. Italiana, 1955, Roma Cremonese (1956), 344–346. (1956) 
  5. Extension du calcul des jets aux jets non holonomes, C. R. Acad. Sci., Paris 239 (1954), 1762–1764. (1954) Zbl0057.15603MR0066734
  6. 10.1007/BF01759302, Ann. Mat. Pura Appl., IV.  Ser. 158 (1991), 151–165. (1991) MR1131848DOI10.1007/BF01759302
  7. A general point of view to nonholonomic jet bundles, Cah. Topol. Géom. Différ. Catég. 44 (2003), 149–160. (2003) MR1985835
  8. Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. (1993) MR1202431
  9. Connections in first principal prolongations, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43 (1996), 163–171. (1996) MR1463518
  10. Lectures on Differential Invariants. Folia Facultatis Scientiarum Naturalium Universitatis Purkynianae Brunensis. Mathematica  1, University J. E.  Purkyně, Brno, 1990. (1990) MR1108622
  11. Introduction to the theory of semi-holonomic jets, Arch. Math. (Brno) 33 (1996), 173–189. (1996) Zbl0915.58004MR1478771
  12. Jet involution and prolongation of connections, Čas. Pěst. Mat. 114 (1989), 356–365. (1989) MR1027231
  13. On the holonomity of higher order connections, Cah. Topol. Géom. Difér. Catég. 12 (1971), 197–212. (1971) Zbl0223.53026MR0305294

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.