| Title:
|
Natural transformations of connections on the first principal prolongation (English) |
| Author:
|
Vondra, Jan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
21-25 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a vector bundle $E\rightarrow M$ and the principal bundle $PE$ of frames of $E$. We determine all natural transformations of the connection bundle of the first order principal prolongation of principal bundle $PE$ into itself. (English) |
| Keyword:
|
natural bundle |
| Keyword:
|
gauge-natural bundle |
| Keyword:
|
natural operator |
| Keyword:
|
principal bundle |
| Keyword:
|
principal connection |
| MSC:
|
53C05 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 06391562 |
| idMR:
|
MR3194765 |
| DOI:
|
10.5817/AM2014-1-21 |
| . |
| Date available:
|
2014-04-04T07:16:21Z |
| Last updated:
|
2015-03-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143716 |
| . |
| Reference:
|
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| Reference:
|
[2] Janyška, J.: Reduction theorems for general linear connections.Differential Geom. Appl. 20 (2) (2004), 177–196. Zbl 1108.53016, MR 2038554, 10.1016/j.difgeo.2003.10.006 |
| Reference:
|
[3] Janyška, J.: Higher order Utiyama invariant interaction.Rep. Math. Phys. 59 (1) (2007), 63–81. MR 2308635, 10.1016/S0034-4877(07)80005-X |
| Reference:
|
[4] Janyška, J., Vondra, J.: Natural principal connections on the principal gauge prolongation of a principal bundle.Rep. Math. Phys. 64 (3) (2009), 395–415. Zbl 1195.53040, MR 2602937, 10.1016/S0034-4877(10)00002-9 |
| Reference:
|
[5] Kolář, I.: Some natural operators in differential geometry.Differential Geometry and Its Aplications (Brno, 1986), Math. Appl. (East European Ser.), Reidel, Dordrecht, 1987, pp. 91–110. MR 0923346 |
| Reference:
|
[6] Kolář, I.: Connections on higher order frame bundles and their gauge analogies.Variations, Geometry and Physics, Nova Science Publishers, 2008, pp. 199–223. MR 2523439 |
| Reference:
|
[7] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry.Springer–Verlag, 1993. MR 1202431 |
| Reference:
|
[8] Krupka, D., Janyška, J.: Lectures on Differential Invariants.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., Brno, 1990. MR 1108622 |
| Reference:
|
[9] Vondra, J.: Classification of principal connections naturally induced on $W^2PE$.Arch. Math. (Brno) 44 (5) (2008), 535–547. Zbl 1212.53040, MR 2501583 |
| . |
