| Title:
|
Some natural operators on vector fields (English) |
| Author:
|
Tomáš, Jiří |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
239-249 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We determine all natural operators transforming vector fields on a manifold $M$ to vector fields on $T^*T^2_1M$, $\operatorname{dim}M \ge 2$, and all natural operators transforming vector fields on $M$ to functions on $T^*TT^2_1M$, $\operatorname{dim}M \ge 3$. We describe some relations between these two kinds of natural operators. (English) |
| Keyword:
|
vector field |
| Keyword:
|
natural bundle |
| Keyword:
|
natural operator |
| Keyword:
|
Weil bundle |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0844.58007 |
| idMR:
|
MR1368261 |
| . |
| Date available:
|
2008-06-06T21:29:06Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107543 |
| . |
| Reference:
|
[1] Cantrijn, F., Crampin, M., Sarlet, W. and Saunders, D.: The canonical isomorphism between $T^kT^*M$ and $T^*T^kM$.C. R. Acad. Sci. Paris 309 (1989), 1509-1514. MR 1033091 |
| Reference:
|
[2] Kobak, P.: Natural liftings of vector fields to tangent bundles of $1$-forms.Mathematica Bohemica 116 (1991), 319-326. MR 1126453 |
| Reference:
|
[3] Kolář, I.: Covariant Approach to Natural Transformations of Weil Bundles.Comment. Math. Univ. Carolinae (1986). MR 0874666 |
| Reference:
|
[4] Kolář, I.: On Cotagent Bundles of Some Natural Bundles.to appear in Rendiconti del Circolo Matematico di Palermo. MR 1344006 |
| Reference:
|
[5] Kolář, I.: On the Natural Operators on Vector Fields.Ann. Global Anal. Geometry 6 (1988), 109-117. MR 0982760 |
| Reference:
|
[6] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer – Verlag, 1993. MR 1202431 |
| Reference:
|
[7] Kolář, I., Radziszewski, Z.: Natural Transformations of Second Tangent and Cotangent Bundles.Czechoslovak Math. (1988), 274-279. MR 0946296 |
| Reference:
|
[8] Modugno, M., Stefani, G.: Some results on second tangent and cotangent spaces.Quaderni dell’Università di Lecce (1978). |
| . |
