| Title:
|
The natural operators lifting vector fields to generalized higher order tangent bundles (English) |
| Author:
|
Mikulski, Włodzimierz M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
207-212 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For natural numbers $r$ and $n$ and a real number $a$ we construct a natural vector bundle $T^{(r),a}$ over $n$-manifolds such that $T^{(r),0}$ is the (classical) vector tangent bundle $T^{(r)}$ of order $r$. For integers $r\ge 1$ and $n\ge 3$ and a real number $a<0$ we classify all natural operators $T_{\vert M_n}\rightsquigarrow TT^{(r),a}$ lifting vector fields from $n$-manifolds to $T^{(r),a}$. (English) |
| Keyword:
|
natural bundle |
| Keyword:
|
natural transformation |
| Keyword:
|
natural operator |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1049.58010 |
| idMR:
|
MR1785038 |
| . |
| Date available:
|
2008-06-06T22:25:53Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107733 |
| . |
| Reference:
|
[1] Doupovec, M.: Natural operators transforming vector fields to the second order tangent bundle.Cas. pest. mat. 115 (1990), 64–72. Zbl 0712.58003, MR 1044015 |
| Reference:
|
[2] Kolář, I.: On the natural operators transforming vector fields to the $r$-th tensor power.Suppl. Rendiconti Circolo Mat. Palermo, 32(II) (1993), 15–20. MR 1283617 |
| Reference:
|
[3] Kolář, I., Michor, P. W., Slovák, J.: Natural operations in differential geometry.Springer-Verlag, Berlin 1993. MR 1202431 |
| Reference:
|
[4] Mikulski, W. M.: Some natural operations on vector fields.Rendiconti Math. Roma 12(VII) (1992), 783–803. Zbl 0766.58005, MR 1205977 |
| Reference:
|
[5] Sekizava, M.: Natural transformations of vector fields on manifolds to vector fields on tangent bundles.Tsukuba J. Math. 12 (1988), 115–128. MR 0949905 |
| . |
