| Title:
|
The natural operators lifting vector fields to $(J\sp rT\sp *)\sp *$ (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:
|
255-260 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For integers $r\ge 2$ and $n\ge 2$ a complete classification of all natural operators $A:T_{\vert M_n}\rightsquigarrow T(J^rT^*)^*$ lifting vector fields to vector fields 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 operators |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1049.58011 |
| idMR:
|
MR1811169 |
| . |
| Date available:
|
2008-06-06T22:26:08Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107739 |
| . |
| Reference:
|
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| Reference:
|
[2] Gancarzewicz, J.: Lifting of functions and vector fields to natural bundles.Dissert. Math. CCXII, Warszawa, 1983. MR 0697471 |
| Reference:
|
[3] Kolář, I.: On natural operators on vector fields.Ann. Global Analysis and Geometry, 6(2) (1988), 109–117. MR 0982760 |
| Reference:
|
[4] 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:
|
[5] Kolář, I., Michor, P. W., Slovák, J.: Natural operations in differential geometry.Springer-Verlag, Berlin 1993. MR 1202431 |
| Reference:
|
[6] Kobak, P.: Natural liftings of vector fields to tangent bundles of bundles of 1-forms.Math. Boch. 116 (1991), 319–326. Zbl 0743.53008, MR 1126453 |
| Reference:
|
[7] Mikulski, W. M.: Some natural operations on vector fields.Rendiconti Math. Roma 12(VII) (1992), 783–803. Zbl 0766.58005, MR 1205977 |
| Reference:
|
[8] Mikulski, W. M.: Some natural constructions on vector fields and higher order cotangent bundles.Mh. Math. 117 (1994), 107–119. Zbl 0796.58002, MR 1266777 |
| Reference:
|
[9] Tomáš, J.: Natural operators on vector fields on the cotangent bundles of the bundles of (k,r)-velocities.Rend. Circ. Mat. Palermo 5431(II) (1998), 113–124 239–249. Zbl 0929.58001, MR 1662732 |
| . |
