| Title:
|
The canonical constructions of connections on total spaces of fibred manifolds (English) |
| Author:
|
Mikulski, Włodzimierz M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2024 |
| Pages:
|
163-175 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We classify classical linear connections $A(\Gamma ,\Lambda ,\Theta )$ on the total space $Y$ of a fibred manifold $Y\rightarrow M$ induced in a natural way by the following three objects: a general connection $\Gamma $ in $Y\rightarrow M$, a classical linear connection $\Lambda $ on $M$ and a linear connection $\Theta $ in the vertical bundle $VY\rightarrow Y$. The main result says that if $ \mathrm{dim}(M)\ge 3$ and $ \mathrm{dim}(Y)-\mathrm{dim}(M) \ge 3$ then the natural operators $A$ under consideration form the $17$ dimensional affine space. (English) |
| Keyword:
|
general connection |
| Keyword:
|
linear connection |
| Keyword:
|
natural operator |
| MSC:
|
53C05 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 07893347 |
| idMR:
|
MR4805419 |
| DOI:
|
10.5817/AM2024-3-163 |
| . |
| Date available:
|
2024-08-02T08:35:47Z |
| Last updated:
|
2025-01-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152524 |
| . |
| Reference:
|
[1] Gancarzewicz, J.: Horizontal lifts of linear connections to the natural vector bundles.Research Notes in Math., vol. 121, Pitman, 1985, pp. 318–341. MR 0864879 |
| Reference:
|
[2] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry.Interscience Publishers New York London, 1963. Zbl 0119.37502, MR 1533559 |
| Reference:
|
[3] Kolář, I.: Induced connections on total spaces of fibred bundles.Int. J. Geom. Methods Mod. Phys. 4 (2010), 705–711. MR 2669064, 10.1142/S021988781000452X |
| Reference:
|
[4] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[5] Mikulski, W.M.: The induced connections on total spaces of fibered manifolds.Publ. Math. (Beograd) 97 (111) (2015), 149–160. MR 3331243, 10.2298/PIM140712001M |
| . |
