| Title:
|
The canonical tensor fields of type $(1,1)$ on $(J^r(\odot ^2 T^{\ast }))^{\ast }$ (English) |
| Author:
|
Michalec, Paweł |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
247-256 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that every natural affinor on $(J^r( \odot ^2 T^{\ast }))^{\ast }(M)$ is proportional to the identity affinor if dim$M\ge 3$. (English) |
| Keyword:
|
natural affinor |
| Keyword:
|
natural bundle |
| Keyword:
|
natural transformation |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1112.58300 |
| idMR:
|
MR2010725 |
| . |
| Date available:
|
2008-06-06T22:42:01Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107871 |
| . |
| Reference:
|
[1] Doupovec M., Kolář I.: Natural affinors on time-dependent Weil bundles.Arch. Math. (Brno) 27 (1991), 205-209. MR 1189217 |
| Reference:
|
[2] Doupovec M., Kurek J.: Torsions of connections of higher order cotangent bundles.Czech. Math. J. (to appear). MR 2018842 |
| Reference:
|
[3] Gancarzewicz J., Kolář I.: Natural affinors on the extended $r$-th order tangent bundles.Suppl. Rendiconti Circolo Mat. Palermo, 1993, 95-100. MR 1246623 |
| Reference:
|
[4] Kolář I., Modugno M.: Torsion of connections on some natural bundles.Diff. Geom. and Appl. 2(1992), 1-16. MR 1244453 |
| Reference:
|
[5] Kolář. I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry.Springer-Verlag, Berlin 1993. Zbl 0782.53013, MR 1202431 |
| 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.: The natural affinors on dual r-jet prolongation of bundles of 2-forms.Ann. UMCS Lublin 2002, (to appear). MR 1984608 |
| Reference:
|
[8] Mikulski W. M.: Natural affinors on $r$-jet prolongation of the tangant bundle.Arch. Math. (Brno) 34 (2) (1998). 321-328. MR 1645340 |
| Reference:
|
[9] Mikulski W. M.: The natural affinors on $ \otimes ^k T^{(k)}$.Note di Matematica vol. 19-n. 2. (1999), 269-274. MR 1816880 |
| Reference:
|
[10] Mikulski W. M.: The natural affinors on generalized higher order tangent bundles.Rend. Mat. Roma vol. 21. (2001). (to appear). Zbl 1048.58004, MR 1884952 |
| Reference:
|
[11] Mikulski W. M.: Natural affinors on $(J^{r,s,q}(\cdot ,{\bold R}^{1,1})_0)^\ast $.Coment. Math. Carolinae 42 (2001), (to appear). Zbl 1050.58004, MR 1883375 |
| Reference:
|
[12] Zajtz A.: On the order of natural operators and liftings.Ann. Polon. Math. 49 (1988), 169-178. MR 0983220 |
| . |
