| Title:
|
Torsions of connections on higher order cotangent bundles (English) |
| Author:
|
Doupovec, Miroslav |
| Author:
|
Kurek, Jan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
949-962 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By a torsion of a general connection $\Gamma $ on a fibered manifold $Y\rightarrow M$ we understand the Frölicher-Nijenhuis bracket of $\Gamma $ and some canonical tangent valued one-form (affinor) on $Y$. Using all natural affinors on higher order cotangent bundles, we determine all torsions of general connections on such bundles. We present the geometrical interpretation and study some properties of the torsions. (English) |
| Keyword:
|
affinor |
| Keyword:
|
general connection |
| Keyword:
|
torsion |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1080.53020 |
| idMR:
|
MR2018842 |
| . |
| Date available:
|
2009-09-24T11:08:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127852 |
| . |
| Reference:
|
[1] M. Doupovec and J. Kurek: Some geometrical constructions with $(0,2)$-tensor fields on higher order cotangent bundles.Annales UMCS 50 (1996), 43–50. MR 1472576 |
| Reference:
|
[2] I. Kolář and M. Modugno: Torsions of connections on some natural bundles.Diff. Geom. Appl. 2 (1992), 1–16. MR 1244453, 10.1016/0926-2245(92)90006-9 |
| Reference:
|
[3] I. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[4] J. Kurek: Natural affinors on higher order cotangent bundle.Arch. Math. (Brno) 28 (1992), 175–180. Zbl 0782.58007, MR 1222284 |
| Reference:
|
[5] J. Kurek: Natural transformations of higher order cotangent bundle functors.Ann. Polon. Math. 58 (1993), 29–35. Zbl 0778.58003, MR 1215758, 10.4064/ap-58-1-29-35 |
| Reference:
|
[6] M. Kureš: Torsions of connections on tangent bundles of higher order.Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II 54 (1998), 65–73. MR 1662727 |
| Reference:
|
[7] L. Mangiarotti and M. Modugno: Fibered spaces, jet spaces and connections for field theories.Proc. of Internat. Meet. Geometry and Physics, Florence 1982, Pitagora Editrice, Bologna, 1983, pp. 135–165. MR 0760841 |
| Reference:
|
[8] L. Mangiarotti and M. Modugno: Connections and differential calculus on fibred manifolds. Applications to field theory.Florence Univ., Dept. of Appl. Math. (1989), Preprint. |
| Reference:
|
[10] A. J. A. Morgan: Higher order tensors.SIAM J. Appl. Math. 30 (1976), 355–380. Zbl 0322.53019, MR 0394482, 10.1137/0130035 |
| Reference:
|
[9] W. M. Mikulski: The natural affinors on generalized hogher order tangent bundles.Rend. Mat. Appl. 21 (2001), 339–349. MR 1884952 |
| . |
