| Title:
|
The natural operators lifting connections to higher order cotangent bundles (English) |
| Author:
|
Mikulski, Włodzimierz M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
509-518 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the problem of finding all ${\mathcal {M} f_m}$-natural operators ${C\colon Q\rightsquigarrow QT^{r*}}$ lifting classical linear connections $\nabla $ on $m$-manifolds $M$ into classical linear connections $C_M(\nabla )$ on the $r$-th order cotangent bundle $T^{r*}M=J^r(M,\mathbb R )_0$ of $M$ can be reduced to the well known one of describing all $\mathcal {M} f_m$-natural operators $D\colon Q\rightsquigarrow \bigotimes ^pT\otimes \bigotimes ^qT^*$ sending classical linear connections $\nabla $ on $m$-manifolds $M$ into tensor fields $D_M(\nabla )$ of type $(p,q)$ on $M$. (English) |
| Keyword:
|
classical linear connection |
| Keyword:
|
natural operator |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 06391509 |
| idMR:
|
MR3277751 |
| DOI:
|
10.1007/s10587-014-0116-7 |
| . |
| Date available:
|
2014-11-10T09:54:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144013 |
| . |
| Reference:
|
[1] Dębecki, J.: Affine liftings of torsion-free connections to Weil bundles.Colloq. Math. 114 (2009), 1-8. MR 2457274, 10.4064/cm114-1-1 |
| Reference:
|
[2] Gancarzewicz, J.: Horizontal lift of connections to a natural vector bundle.Differential Geometry Proc. 5th Int. Colloq., Santiago de Compostela, Spain, 1984, Res. Notes Math. 131 Pitman, Boston (1985), 318-341 L. A. Cordero. Zbl 0646.53028, MR 0864879 |
| Reference:
|
[3] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. I.Interscience Publishers, New York (1963). Zbl 0119.37502, MR 0152974 |
| Reference:
|
[4] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer Berlin (1993). MR 1202431 |
| Reference:
|
[5] Kurek, J., Mikulski, W. M.: The natural operators lifting connections to tensor powers of the cotangent bundle.Miskolc Math. Notes 14 (2013), 517-524. MR 3144087, 10.18514/MMN.2013.911 |
| Reference:
|
[6] Kureš, M.: Natural lifts of classical linear connections to the cotangent bundle.J. Slovák Proc. of the 15th Winter School on geometry and physics, Srní, 1995, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43 (1996), 181-187. Zbl 0905.53018, MR 1463520 |
| Reference:
|
[7] Mikulski, W. M.: The natural bundles admitting natural lifting of linear connections.Demonstr. Math. 39 (2006), 223-232. Zbl 1100.58001, MR 2223893, 10.1515/dema-2006-0127 |
| . |
