| Title:
|
Some functorial prolongations of general connections (English) |
| Author:
|
Kolář, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
111-117 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the problem of prolongating general connections on arbitrary fibered manifolds with respect to a product preserving bundle functor. Our main tools are the theory of Weil algebras and the Frölicher-Nijenhuis bracket. (English) |
| Keyword:
|
general connection |
| Keyword:
|
tangent valued form |
| Keyword:
|
functorial prolongation |
| Keyword:
|
Weil functor |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 06890308 |
| idMR:
|
MR3813738 |
| DOI:
|
10.5817/AM2018-2-111 |
| . |
| Date available:
|
2018-06-05T13:37:53Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147217 |
| . |
| Reference:
|
[1] Cabras, A., Kolář, I.: Prolongation of tangent valued forms to Weil bundles.Arch. Math. (Brno) 31 (1995), 139–145. MR 1357981 |
| Reference:
|
[2] Ehresmann, C.: Oeuvres complètes et commentés.Cahiers Topol. Géom. Diff. XXIV (Suppl. 1 et 2) (1983). |
| Reference:
|
[3] Kolář, I.: Handbook of Global Analysis.ch. Weil Bundles as Generalized Jet Spaces, pp. 625–665, Elsevier, Amsterdam, 2008. MR 2389643 |
| Reference:
|
[4] Kolář, I.: On the functorial prolongations of fiber bundles.Miskolc Math. Notes 14 (2013), 423–431. MR 3144079, 10.18514/MMN.2013.903 |
| Reference:
|
[5] Kolář, I.: Covariant Approach to Weil Bundles.Folia, Masaryk University, Brno (2016). |
| Reference:
|
[6] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry.Springer Verlag, 1993. |
| Reference:
|
[7] Mangiarotti, L., Modugno, M.: Graded Lie algebras and connections on a fibered space.J. Math. Pures Appl. (9) 63 (1984), 111–120. |
| Reference:
|
[8] Weil, A.: Théorie des points proches sur les variétes différentielles.Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. |
| . |
