| Title:
|
The jet prolongations of $2$-fibred manifolds and the flow operator (English) |
| Author:
|
Mikulski, Włodzimierz M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
17-21 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $r$, $s$, $m$, $n$, $q$ be natural numbers such that $s\ge r$. We prove that any $2$-${\mathcal{F}}\mathbb{M}_{m,n,q}$-natural operator $A\colon T_{\operatorname{2-proj}}\rightsquigarrow TJ^{(s,r)}$ transforming $2$-projectable vector fields $V$ on $(m,n,q)$-dimensional $2$-fibred manifolds $Y\rightarrow X\rightarrow M$ into vector fields $A(V)$ on the $(s,r)$-jet prolongation bundle $J^{(s,r)}Y$ is a constant multiple of the flow operator $\mathcal{J}^{(s,r)}$. (English) |
| Keyword:
|
$(s,r)$-jet |
| Keyword:
|
bundle functor |
| Keyword:
|
natural operator |
| Keyword:
|
flow operator |
| Keyword:
|
$2$-fibred manifold |
| Keyword:
|
$2$-projectable vector field |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 1212.58003 |
| idMR:
|
MR2431227 |
| . |
| Date available:
|
2008-06-06T22:52:33Z |
| Last updated:
|
2014-06-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108092 |
| . |
| Reference:
|
[1] Cabras, A., Janyška, J., Kolář, I.: On the geometry of variational calculus on some functional bundles.Note Mat. 26 (2) (2006), 51–57. Zbl 1195.58007, MR 2298069 |
| Reference:
|
[2] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry.Springer-Verlag Berlin, 1993. MR 1202431 |
| Reference:
|
[3] Mikulski, W. M.: The jet prolongations of fibered manifolds and the flow operator.Publ. Math. Debrecen 59 (2001), 441–458. MR 1874443 |
| Reference:
|
[4] Mikulski, W. M.: The natural operators lifting projectable vector fields to some fiber product preserving bundles.Ann. Polon. Math. 81 (3) (2003), 261–271. Zbl 1099.58003, MR 2044627, 10.4064/ap81-3-4 |
| . |
