| Title:
|
On the $\gamma $-equivalence of semiholonomic jets (English) |
| Author:
|
Doupovec, Miroslav |
| Author:
|
Kolář, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
261-264 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well known that the concept of holonomic $r$-jet can be geometrically characterized in terms of the contact of individual curves. However, this is not true for the semiholonomic $r$-jets, [5], [8]. In the present paper, we discuss systematically the semiholonomic case. (English) |
| Keyword:
|
jet bundle |
| Keyword:
|
semiholonomic $r$-jet |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 07144741 |
| idMR:
|
MR4038361 |
| DOI:
|
10.5817/AM2019-4-261 |
| . |
| Date available:
|
2019-10-30T08:56:42Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147879 |
| . |
| Reference:
|
[1] Cabras, A., Kolář, I.: Prolongation of tangent valued forms.Arch. Math. (Brno) 38 (2002), 243–254. MR 1942654 |
| Reference:
|
[2] Doupovec, M., Mikulski, W.M.: Holonomic extension of connections and symmetrization of jets.Rep. Math. Phys. 60 (2007), 299–316. Zbl 1160.58001, MR 2374824, 10.1016/S0034-4877(07)80141-8 |
| Reference:
|
[3] Ehresmann, C.: Extension du calcul des jets aux jets non holonomes.CRAS Paris 239 (1954), 1762–1764. Zbl 0057.15603, MR 0066734 |
| Reference:
|
[4] Ehresmann, C.: Sur les connexions d’ordre supériour.Atti del V. Cong. dell Unione Mat. Italiana, Roma Cremonese (1956), 326–328. |
| Reference:
|
[5] Kolář, I.: The contact of spaces with connection.J. Differential Geometry 7 (1972), 563–570. Zbl 0273.53025, MR 0415660, 10.4310/jdg/1214431173 |
| Reference:
|
[6] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry.Springer Verlag, 1993. |
| Reference:
|
[7] Libermann, P.: Prolongations des fibrés principaux et groupoides différentiables.Sémin. Analyse Globale Montréal, 1969, pp. 7–108. MR 0356117 |
| Reference:
|
[8] Libermann, P.: Introduction to the theory of semiholonomic jets.Arch. Math. (Brno) 33 (1997), 173–189. MR 1478771 |
| Reference:
|
[9] Libermann, P.: Charles Ehresmann’s concepts in differential geometry.Banach Center Publications 76 (2007), 35–50, Polish Academy of Sciences, Warszawa. MR 2342844, 10.4064/bc76-0-2 |
| . |
