| Title:
|
On the existence of prolongation of connections (English) |
| Author:
|
Doupovec, Miroslav |
| Author:
|
Mikulski, Włodzimierz M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
1323-1334 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We classify all bundle functors $G$ admitting natural operators transforming connections on a fibered manifold $Y\rightarrow M$ into connections on $GY\rightarrow M$. Then we solve a similar problem for natural operators transforming connections on $Y\rightarrow M$ into connections on $GY\rightarrow Y$. (English) |
| Keyword:
|
bundle functor |
| Keyword:
|
connection |
| Keyword:
|
natural operator |
| MSC:
|
58A05 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1164.58300 |
| idMR:
|
MR2280811 |
| . |
| Date available:
|
2009-09-24T11:43:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128147 |
| . |
| Reference:
|
[1] M. Doupovec and I. Kolář: On natural operators transforming connections to the tangent bundle of a fibred manifold.Knižnice VUT Brno B-119 (1988), 47–56. |
| Reference:
|
[2] M. Doupovec and I. Kolář: Iteration of fiber product preserving bundle functors.Monatshefte Math. 134 (2001), 39–50. MR 1872045, 10.1007/s006050170010 |
| Reference:
|
[3] M. Doupovec and W. M. Mikulski: Prolongation of pairs of connections into connections on vertical bundles.Arch. Math. (Brno) 41 (2005), 409–422. MR 2195494 |
| Reference:
|
[4] J. Janyška and M. Modugno: Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibered manifold.Arch. Math. (Brno) 32 (1996), 281–288. MR 1441399 |
| Reference:
|
[5] I. Kolář: Some natural operations with connections.Jour. Nat. Math. India 5 (1987), 127–141. MR 0994555 |
| Reference:
|
[6] I. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[7] I. Kolář and W. M. Mikulski: Natural lifting of connections to vertical bundles.Rend. Circ. Mat. Palermo, Serie II, Suppl. 63 (2000), 97–102. MR 1758084 |
| Reference:
|
[8] W. M. Mikulski: Non-existence of some canonical constructions on connections.Comment Math. Univ. Carolinae 44.4 (2003), 691–695. Zbl 1099.58004, MR 2062885 |
| Reference:
|
[9] W. M. Mikulski: Non-existence of natural operators transforming connections on $Y\rightarrow M$ into connections on $FY\rightarrow Y$.Arch. Math. (Brno) 41 (2005), 1–4. MR 2142138 |
| Reference:
|
[10] A. Vondra: Higher-order differential equations represented by connections on prolongations of a fibered manifold.Extracta Math. 15.3 (2000), 421–512. Zbl 0992.34006, MR 1825970 |
| . |
