| Title:
|
Special tangent valued forms and the Frölicher-Nijenhuis bracket (English) |
| Author:
|
Cabras, Antonella |
| Author:
|
Kolář, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
71-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define the tangent valued $C$-forms for a large class of differential geometric categories. We deduce that the Frölicher-Nijenhuis bracket of two tangent valued $C$-forms is a $C$-form as well. Then we discuss several concrete cases and we outline the relations to the theory of special connections. (English) |
| Keyword:
|
category over manifolds |
| Keyword:
|
tangent valued form |
| Keyword:
|
Frölicher-Nijenhuis bracket |
| Keyword:
|
special connections |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0801.53014 |
| idMR:
|
MR1242630 |
| . |
| Date available:
|
2008-06-06T21:23:56Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107468 |
| . |
| Reference:
|
[1] Cabras, A., Canarutto, D.: Systems of Principal Tangent-valued forms.Rendiconti di Mat., Ser VII, Roma 11 (1991), 471-493. MR 1136517 |
| Reference:
|
[2] Cabras, A., Canarutto, D.: The System of Principal Connections.Rendiconti di Mat., Ser VII, Roma 11 (1991), 849-871. MR 1151603 |
| Reference:
|
[3] Cabras, A., Canarutto, D., Kolář, I., Modugno, M.: Structured Bundles.Pitagora Editrice, Bologna (1991). |
| Reference:
|
[4] Crampin, M., Ibort, L. A.: Graded Lie algebra of derivations and Ehresmann connections.J. Math. Pures Appl. 66 (1987), 113-125. MR 0884816 |
| Reference:
|
[5] Frölicher, A., Nijenhuis, A.: Theory of vector valued differential forms I..Indag. Math. 18 (1956), 338-385. |
| Reference:
|
[6] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer - Verlag, 1993. MR 1202431 |
| Reference:
|
[7] Kolář, I., Modugno, M.: On the algebraic structure of the bundles of higher velocities.Seminari Instituto di Mat. Appl. “G. Sansone”, Florence (1989), 17 pp. |
| Reference:
|
[8] Kolář, I., Modugno, M.: On the algebraic structure on the jet prolongations of fibred manifolds.Czechoslovak Math. J. 40 (1990), 601-611. MR 1084896 |
| Reference:
|
[9] Michor, P. W.: Remarks on the Frölicher-Nijenhuis bracket.Diff. Geom. and Its Applications, Proc. Conf. J.E. Purkyně University, Brno (1987), 197-220. Zbl 0633.53024, MR 0923350 |
| Reference:
|
[10] Modugno, M.: Systems of vector valued forms on a fibred manifold and applications to gauge theories.Proc. Conf. Diff. Geom. Math. in Math. Phys., Salamanca 1985, Lect. Not. Math. 1251, Springer, 1987, 238-264. Zbl 0614.53072, MR 0897122 |
| . |
