| Title:
|
Non-existence of some canonical constructions on connections (English) |
| Author:
|
Mikulski, W. M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
691-695 |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a vector bundle functor $H:\Cal M f\to \Cal V\Cal B$ with the point property we prove that $H$ is product preserving if and only if for any $m$ and $n$ there is an $\Cal F\Cal M_{m,n}$-natural operator $D$ transforming connections $\Gamma$ on $(m,n)$-dimensional fibered manifolds $p:Y\to M$ into connections $D(\Gamma)$ on $Hp:HY\to HM$. For a bundle functor $E:\Cal F\Cal M_{m,n}\to \Cal F\Cal M$ with some weak conditions we prove non-existence of $\Cal F\Cal M_{m,n}$-natural operators $D$ transforming connections $\Gamma$ on $(m,n)$-dimensional fibered manifolds $Y\to M$ into connections $D(\Gamma)$ on $EY\to M$. (English) |
| Keyword:
|
(general) connection |
| Keyword:
|
natural operator |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1099.58004 |
| idMR:
|
MR2062885 |
| . |
| Date available:
|
2009-01-08T19:32:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119423 |
| . |
| Reference:
|
[1] Doupovec M., Mikulski W.M: Horizontal extension of connections into $(2)$-connections.to appear. MR 2103898 |
| Reference:
|
[2] Kolář I.: On generalized connections.Beiträge Algebra Geom. 11 (1981), 29-34. MR 0680454 |
| Reference:
|
[3] Kolář I., Michor P.W., Slovák J.: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993. MR 1202431 |
| Reference:
|
[4] Kolář I., Mikulski W.M.: Natural lifting of connections to vertical bundles.Suppl. Rend. Circolo Math. Palermo II 63 (2000), 97-102. MR 1758084 |
| Reference:
|
[5] Mikulski W.M.: Non-existence of a connection on $FY\to Y$ canonically dependent on a connection on $Y\to M$.Arch. Math. Brno, to appear. MR 2142138 |
| Reference:
|
[6] Slovák J.: Prolongations of connections and sprays with respect to Weil functors.Suppl. Rend. Circ. Mat. Palermo, Serie II 14 (1987), 143-155. MR 0920852 |
| . |
