| Title:
|
Natural transformations of semi-holonomic 3-jets (English) |
| Author:
|
Vosmanská, Gabriela |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
313-318 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\bar{J}^3$ be the functor of semi-holonomic $3$-jets and $\bar{J}^{3,2}$ be the functor of those semi-holonomic $3$-jets, which are holonomic in the second order. We deduce that the only natural transformations $\bar{J}^3 \rightarrow \bar{J}^3$ are the identity and the contraction. Then we determine explicitely all natural transformations $\bar{J}^{3,2}\rightarrow \bar{J}^{3,2}$, which form two $5$-parameter families. (English) |
| Keyword:
|
semi-holonomic 3-jet |
| Keyword:
|
natural transformation |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0852.58003 |
| idMR:
|
MR1390591 |
| . |
| Date available:
|
2008-06-06T21:29:44Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107553 |
| . |
| Reference:
|
[1] Ehresmann, C.: Extension du calcul des jets aux jets non-holonomes.C.R.Acad. Sci. Paris, 239 (1954), 1762-1764. Zbl 0057.15603, MR 0066734 |
| Reference:
|
[2] Kolř, I.: The contact of spaces with connection.J. Differential Geometry 7 (1972), 563-570. MR 0415660 |
| Reference:
|
[3] Kolř, I., Michor, P., Slov k, J.: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[4] Kolř, I., Vosmansk , G.: Natural operations with second order jets.Rendiconti del Circolo Matematico di Palermo, Serie II, n. 14 (1987), 179-186. MR 0920854 |
| Reference:
|
[5] Kolř, I., Vosmansk , G.: Natural transformations of higher order tangent bundles and jet spaces.Čas. pěst. mat. 114 (1989), 181-186. MR 1063764 |
| Reference:
|
[6] Virsik, G.: Total connections in Lie groupoids.Arch. Math. (Brno), 31 (1995), 183-200. Zbl 0841.53024, MR 1368257 |
| . |
