| Title:
|
On special types of semiholonomic $3$-jets (English) |
| Author:
|
Kolář, Ivan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
165-175 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
First we summarize some properties of the nonholonomic $r$-jets from the functorial point of view. In particular, we describe the basic properties of our original concept of nonholonomic $r$-jet category. Then we deduce certain properties of the Weil algebras associated with nonholonomic $r$-jets. Next we describe an algorithm for finding the nonholonomic $r$-jet categories. Finally we classify all special types of semiholonomic $3$-jets. (English) |
| Keyword:
|
special type of nonholonomic $r$-jet |
| Keyword:
|
nonholonomic $r$-jet category |
| Keyword:
|
classification of semiholonomic $3$-jet |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1274.58001 |
| idMR:
|
MR3035504 |
| DOI:
|
10.1007/s10587-013-0011-7 |
| . |
| Date available:
|
2013-03-01T16:12:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143177 |
| . |
| Reference:
|
[1] Ehresmann, C.: Oeuvres Complètes et Commentées. Topologie Algébrique et Géométrie Différentielle. Parties I-1 et I-2. Éd. par Andrée Charles Ehresmann, Suppléments 1 et 2 au Vol. XXIV.Cahiers de Topologie et Géométrie Différentielle (1983), French. |
| Reference:
|
[2] Kolář, I.: The contact of spaces with connection.J. Differ. Geom. 7 (1972), 563-570. Zbl 0273.53025, MR 0415660, 10.4310/jdg/1214431173 |
| Reference:
|
[3] Kolář, I.: Bundle functors of the jet type.Differential Geometry and Applications. Proceedings of the 7th international conference Masaryk University, Brno (1999), 231-237. Zbl 0951.58003, MR 1708910 |
| Reference:
|
[4] Kolář, I.: A general point of view to nonholonomic jet bundles.Cah. Topol. Géom. Différ. Catég. 44 (2003), 149-160. Zbl 1048.58002, MR 1985835 |
| Reference:
|
[5] Kolář, I.: Weil Bundles as Generalized Jet Spaces.Handbook of global analysis Amsterdam: Elsevier (2008), 625-665. Zbl 1236.58010, MR 2389643 |
| Reference:
|
[6] Kolář, I.: On special types of nonholonomic contact elements.Differ. Geom. Appl. 29 (2011), 135-140. Zbl 1229.58005, MR 2831821, 10.1016/j.difgeo.2011.03.007 |
| Reference:
|
[7] Kolář, I., Mikulski, W. M.: On the fiber product preserving bundle functors.Differ. Geom. Appl. 11 (1999), 105-115. MR 1712139, 10.1016/S0926-2245(99)00022-4 |
| Reference:
|
[8] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer, Berlin (1993). MR 1202431 |
| Reference:
|
[9] Libermann, P.: Introduction to the theory of semi-holonomic jets.Arch. Math., Brno 33 (1997), 173-189. MR 1478771 |
| Reference:
|
[10] Vosmanská, G.: Natural transformations of semi-holonomic $3$-jets.Arch. Math., Brno 31 (1995), 313-318. Zbl 0852.58003, MR 1390591 |
| . |
