| Title:
|
Invariant subspaces in higher order jet prolongations of a fibred manifold (English) |
| Author:
|
Doupovec, Miroslav |
| Author:
|
Vondra, Alexandr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
209-220 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a generalization of the concept of semiholonomic jets within the framework of higher order prolongations of a fibred manifold. In this respect, a compilation of our 2-fibred manifold approach with the methods of natural operators theory is used. (English) |
| Keyword:
|
2-fibred manifold |
| Keyword:
|
jet prolongation |
| Keyword:
|
semiholonomic jets |
| Keyword:
|
natural transformation |
| Keyword:
|
connection |
| MSC:
|
53A55 |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 1038.58001 |
| idMR:
|
MR1745473 |
| . |
| Date available:
|
2009-09-24T10:31:49Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127562 |
| . |
| Reference:
|
[1] M. Doupovec and A. Vondra: On certain natural transformations between connections.Proc. Conf. Diff. Geom. and Its Appl., Opava, 1992, Silesian University, Opava, 1993, pp. 273–279. MR 1255548 |
| Reference:
|
[2] M. Doupovec and A. Vondra: Some natural operations between connections on fibered manifolds.Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II 39 (1996), 73–84. MR 1396603 |
| Reference:
|
[3] M. Doupovec and A. Vondra: Natural relations between connections in $2$-fibred manifolds.New Developments in Differential Geometry, Proceedings, Kluwer Academic Publishers, Dordrecht, 1996, pp. 113–130. MR 1377278 |
| Reference:
|
[4] I. Kolář: Connections in 2-fibred manifolds.Arch. Math. (Brno) 17 (1981), 23–30. |
| Reference:
|
[5] I. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry.Springer Verlag, 1993. MR 1202431 |
| Reference:
|
[6] D. Krupka and J. Janyška: Lectures on differential invariants.Folia Fac. Sci. Natur. Univ. Purk. Brun. Phys., Brno, 1990. MR 1108622 |
| Reference:
|
[7] L. Mangiarotti and M. Modugno: Fibred spaces, jet spaces and connections for field theories.Proceedings of International Meeting “Geometry and Physics”, Florence, 1982, Pitagora Editrice, Bologna, 1983, pp. 135–165. MR 0760841 |
| Reference:
|
[8] L. Mangiarotti and M. Modugno: Connections and differential calculus on fibred manifolds. Aplications to field theory.Istituto di Matematica Applicata “G. Sansone", Firense, 1989, 1–147. |
| Reference:
|
[9] D. J. Saunders: The Geometry of Jet Bundles.London Mathematical Society Lecture Note Series 142, Cambridge University Press, Cambridge, 1989. Zbl 0665.58002, MR 0989588 |
| Reference:
|
[10] A. Vondra: Towards a geometry of higher-order partial differential equations represented by connections on fibered manifolds.Brno, 1995, 1–114. |
| . |
