| Title:
|
Tangent Dirac structures of higher order (English) |
| Author:
|
Kouotchop Wamba, P. M. |
| Author:
|
Ntyam, A. |
| Author:
|
Wouafo Kamga, J. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
17-22 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $L$ be an almost Dirac structure on a manifold $M$. In [2] Theodore James Courant defines the tangent lifting of $L$ on $TM$ and proves that:
If $L$ is integrable then the tangent lift is also integrable.
In this paper, we generalize this lifting to tangent bundle of higher order. (English) |
| Keyword:
|
Dirac structure |
| Keyword:
|
almost Dirac structure |
| Keyword:
|
tangent functor of higher order |
| Keyword:
|
natural transformations |
| MSC:
|
53C15 |
| MSC:
|
53C75 |
| MSC:
|
53D05 |
| idZBL:
|
Zbl 1240.53058 |
| idMR:
|
MR2813543 |
| . |
| Date available:
|
2011-05-23T12:14:51Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141506 |
| . |
| Reference:
|
[1] Cantrijn, F., Crampin, M., Sarlet, W., Saunders, D.: The canonical isomorphism between $T^{k}T^{\ast }$ and $T^{\ast }T^{k}$.C. R. Acad. Sci., Paris, Sér. II 309 (1989), 1509–1514. MR 1033091 |
| Reference:
|
[2] Courant, T.: Tangent Dirac Structures.J. Phys. A: Math. Gen. 23 (22) (1990), 5153–5168. Zbl 0715.58013, MR 1085863, 10.1088/0305-4470/23/22/010 |
| Reference:
|
[3] Courant, T.: Tangent Lie Algebroids.J. Phys. A: Math. Gen. 27 (13) (1994), 4527–4536. Zbl 0843.58044, MR 1294955, 10.1088/0305-4470/27/13/026 |
| Reference:
|
[4] Gancarzewicz, J., Mikulski, W., Pogoda, Z.: Lifts of some tensor fields and connections to product preserving functors.Nagoya Math. J. 135 (1994), 1–41. Zbl 0813.53010, MR 1295815 |
| Reference:
|
[5] Grabowski, J., Urbanski, P.: Tangent lifts of Poisson and related structures.J. Phys. A: Math. Gen. 28 (23) (1995), 6743–6777. Zbl 0872.58028, MR 1381143, 10.1088/0305-4470/28/23/024 |
| Reference:
|
[6] Kolář, I., Michor, P., Slovák, J.: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[7] Morimoto, A.: Lifting of some type of tensors fields and connections to tangent bundles of $p^{r}$-velocities.Nagoya Math. J. 40 (1970), 13–31. MR 0279720 |
| Reference:
|
[8] Ntyam, A., Wouafo Kamga, J.: New versions of curvatures and torsion formulas of complete lifting of a linear connection to Weil bundles.Ann. Pol. Math. 82 (3) (2003), 233–240. MR 2040808, 10.4064/ap82-3-4 |
| . |
