| Title:
|
Lifting of projectable vector fields to vertical fiber product preserving vector bundles (English) |
| Author:
|
Mikulski, Włodzimierz M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
265-271 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles. (English) |
| Keyword:
|
fibered manifolds |
| Keyword:
|
vector bundle functors |
| Keyword:
|
natural operators |
| Keyword:
|
natural transformations |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1164.58303 |
| idMR:
|
MR2260386 |
| . |
| Date available:
|
2008-06-06T22:48:25Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108006 |
| . |
| Reference:
|
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| Reference:
|
[2] Kolář, I.: On the natural operators transforming vector fields to the $r$-th tensor power.Suppl. Rend. Math. Circ. Palermo II(32) (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] Kolář, I., Mikulski, W. M.: On the fiber product preserving bundle functors.Differential Geom. Appl. 11 (1999), 105–115.. MR 1712139 |
| Reference:
|
[5] Kurek, J., Mikulski, W. M.: Lifting of linear vector fields to fiber product preserving vertical gauge bundles.Colloq. Math. 103(1) (2005), 33–40. MR 2148947 |
| Reference:
|
[6] Mikulski, W. M.,: Some natural constructions on vector fields and higher order cotangent bundles.Monatsh. Math. 117 (1994), 107–115. Zbl 0796.58002, MR 1266777 |
| Reference:
|
[7] Mikulski, W. M.,: Some natural operations on vector fields.Rend. Mat. Roma 12 (1992), 783–803. Zbl 0766.58005, MR 1205977 |
| Reference:
|
[8] 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 |
| . |
