| Title:
|
The natural affinors on $(J^rT^*)^*$ (English) |
| Author:
|
Mikulski, Włodzimierz M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
261-267 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For natural numbers $r$ and $n\ge 2$ a complete classification of natural affinors on the natural bundle $(J^rT^*)^*$ dual to $r$-jet prolongation $J^rT^*$ of the cotangent bundle over $n$-manifolds is given. (English) |
| Keyword:
|
bundle functors |
| Keyword:
|
natural transformations |
| Keyword:
|
natural affinors |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1049.58012 |
| idMR:
|
MR1811170 |
| . |
| Date available:
|
2008-06-06T22:26:11Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107740 |
| . |
| Reference:
|
[1] Doupovec, M.: Natural transformations between $TTT^*M$ and $TT^*TM$.Czechoslovak Math. J. 43 (118) 1993, 599–613. Zbl 0806.53024, MR 1258423 |
| Reference:
|
[2] Doupovec, M., Kolář, I.: Natural affinors on time-dependent Weil bundles.Arch. Math. (Brno) 27 (1991), 205–209. MR 1189217 |
| Reference:
|
[3] Gancarzewicz, J., Kolář, I.: Natural affinors on the extended $r$-th order tangent bundles.Suppl. Rendiconti Circolo Mat. Palermo, 30 (1993), 95–100. MR 1246623 |
| Reference:
|
[4] Kolář I., Michor P. W., Slovák J.: Natural operations in differential geometry.Springer-Verlag, Berlin 1993. MR 1202431 |
| Reference:
|
[5] Kolář, I., Modugno, M.: Torsions of connections on some natural bundles.Diff. Geom. and Appl. 2(1992), 1–16. MR 1244453 |
| Reference:
|
[6] Kurek, J.: Natural affinors on higher order cotangent bundles.Arch. Math. (Brno) 28 (1992), 175–180. MR 1222284 |
| Reference:
|
[7] Mikulski, W. M.: Natural affinors on $r$-jet prolongation of the tangent bundle.Arch. Math. (Brno) 34(2)(1998), 321–328. Zbl 0915.58006, MR 1645340 |
| Reference:
|
[8] Mikulski, W. M.: The natural affinors on $\otimes ^k T^{(r)}$.Note di Matematica, to appear. |
| Reference:
|
[9] Zajtz, A.: On the order of natural operators and liftings.Ann. Polon. Math. 49(1988), 169–178. MR 0983220 |
| . |
