| Title:
|
Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle (English) |
| Author:
|
Mikulski, W. M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
565-573 |
| . |
| Category:
|
math |
| . |
| Summary:
|
For natural numbers $r$ and $n\geq 2$ all natural operators $T_{\vert \Cal M f_n}\rightsquigarrow T^* (J^rT^{*})$ transforming vector fields from $n$-manifolds $M$ into $1$-forms on $J^r T^{*}M=\{j^r_x (\omega)\mid \omega \in \Omega^1(M), x\in M\}$ are classified. A similar problem with fibered manifolds instead of manifolds is discussed. (English) |
| Keyword:
|
natural bundle |
| Keyword:
|
natural operator |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1090.58005 |
| idMR:
|
MR1920532 |
| . |
| Date available:
|
2009-01-08T19:25:16Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119346 |
| . |
| Reference:
|
[1] Doupovec M., Kurek J.: Liftings of tensor fields to the cotangent bundles.Proc. Conf. Differential Geom. and Appl., Brno, 1995, pp.141-150. MR 1406334 |
| Reference:
|
[2] Kolář I., Michor P.W., Slovák J.: Natural Operations in Differential Geometry.Springer Verlag, Berlin, 1993. MR 1202431 |
| Reference:
|
[3] Kurek J., Mikulski W.M.: The natural operators lifting $1$-forms to some vector bundle functors.Colloq. Math. (2002), to appear. Zbl 1020.58003, MR 1930803 |
| Reference:
|
[4] Mikulski W.M.: The natural operators $T_{\vert \Cal M f_n} \rightsquigarrow T^* T^{r*}$ and $T_{\vert \Cal M f_n}\rightsquigarrow \Lambda^2 T^*T^{r*}$.Colloq. Math. (2002), to appear. MR 1930256 |
| Reference:
|
[5] Mikulski W.M.: Liftings of $1$-forms to the bundle of affinors.Ann. UMCS Lublin (LV)(A) (2001), 109-113. Zbl 1020.58005, MR 1845255 |
| . |
