Geodesic
Higher order jet involution
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 933-945 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 58A05, 58A20
Keywords: jet prolongation; classical linear connection; higher order connection 
@article{CMJ_2007_57_3_a11,
     author = {Doupovec, M. and Mikulski, W. M.},
     title = {Higher order jet involution},
     journal = {Czechoslovak Mathematical Journal},
     pages = {933--945},
     year = {2007},
     volume = {57},
     number = {3},
     mrnumber = {2356931},
     zbl = {1174.58001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a11/}
}
TY  - JOUR
AU  - Doupovec, M.
AU  - Mikulski, W. M.
TI  - Higher order jet involution
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 933
EP  - 945
VL  - 57
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a11/
LA  - en
ID  - CMJ_2007_57_3_a11
ER  - 
%0 Journal Article
%A Doupovec, M.
%A Mikulski, W. M.
%T Higher order jet involution
%J Czechoslovak Mathematical Journal
%D 2007
%P 933-945
%V 57
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a11/
%G en
%F CMJ_2007_57_3_a11
Doupovec, M.; Mikulski, W. M. Higher order jet involution. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 933-945. http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a11/

[1] A.  Cabras, I. Kolář: Prolongation of second order connections to vertical Weil bundles. Arch. Math., Brno 37 (2001), 333–347. | MR

[2] M. Doupovec, I. Kolář: Iteration of fiber product preserving bundle functors. Monatsh. Math. 134 (2001), 39–50. | DOI | MR

[3] M.  Doupovec, W. M. Mikulski: On involutions of iterated bundle functors. Colloq. Math 106 (2006), 135–145. | DOI | MR

[4] C.  Ehresmann: Sur les connexions d’ordre supérieur. Atti del V.  Cong. del’Unione Mat. Italiana, 1955, Roma Cremonese (1956), 344–346.

[5] C. Ehresmann: Extension du calcul des jets aux jets non holonomes. C. R. Acad. Sci., Paris 239 (1954), 1762–1764. | MR | Zbl

[6] I.  Kolář, M. Modugno: Natural maps on the iterated jet prolongation of a fibered manifold. Ann. Mat. Pura Appl., IV.  Ser. 158 (1991), 151–165. | DOI | MR

[7] I.  Kolář: A general point of view to nonholonomic jet bundles. Cah. Topol. Géom. Différ. Catég. 44 (2003), 149–160. | MR

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

[9] I. Kolář, G. Virsik: Connections in first principal prolongations. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43 (1996), 163–171. | MR

[10] D.  Krupka, J. Janyška: Lectures on Differential Invariants. Folia Facultatis Scientiarum Naturalium Universitatis Purkynianae Brunensis. Mathematica  1. University J. E.  Purkyně, Brno, 1990. | MR

[11] P. Libermann: Introduction to the theory of semi-holonomic jets. Arch. Math. (Brno) 33 (1996), 173–189. | MR | Zbl

[12] M. Modugno: Jet involution and prolongation of connections. Čas. Pěst. Mat. 114 (1989), 356–365. | MR

[13] G. Virsik: On the holonomity of higher order connections. Cah. Topol. Géom. Difér. Catég. 12 (1971), 197–212. | MR | Zbl