| Title:
|
Double vector bundles and duality (English) |
| Author:
|
Konieczna, Katarzyna |
| Author:
|
Urbański, Pawel |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
59-95 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notions of the dual double vector bundle and the dual double vector bundle morphism are defined. Theorems on canonical isomorphisms are formulated and proved. Several examples are given. (English) |
| Keyword:
|
double vector bundles |
| Keyword:
|
duality |
| MSC:
|
53C15 |
| MSC:
|
53C80 |
| MSC:
|
53D05 |
| MSC:
|
53D17 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 1054.53055 |
| idMR:
|
MR1684522 |
| . |
| Date available:
|
2008-06-06T22:22:37Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107684 |
| . |
| Reference:
|
[1] Grabowski, J., Urbański, P.: Tangent lifts of Poisson and related structures.J. Phys. A. 28 (1995), 6743–6777. MR 1381143 |
| Reference:
|
[2] Mackenzie, K. C. H.: Double Lie algebroids and second-order geometry I.Adv. Math. 94 (1992), 180-239. Zbl 0765.57025, MR 1174393 |
| Reference:
|
[3] Pradines, J.: Géométrie differentielle au-dessus d’un grupoïde.C. R. Acad. Sci. Paris, série A 266 (1968), 1194-1196. MR 0231306 |
| Reference:
|
[4] Pradines, J.: Représentation des jets non holonomes par des morphismes vectoriels doubles soudés.C. R. Acad. Sci. Paris, série A 278 (1974), 1523-1526. Zbl 0285.58002, MR 0388432 |
| Reference:
|
[5] Tulczyjew, W. M.: Geometric Formulations of Physical Theories.Bibliopolis, Napoli, 1989. Zbl 0707.58001, MR 1026453 |
| Reference:
|
[6] Tulczyjew, W. M.: Les sous-varieétés lagrangiennes et la dynamique lagrangienne.C. R. Acad. Sci. Paris, série A 283 (1976), 675-678. MR 0420715 |
| Reference:
|
[7] Tulczyjew, W. M.: Les sous-varieétés lagrangiennes et la dynamique hamiltonienne.C. R. Acad. Sci. Paris, série A 283 (1976), 15-18. MR 0420714 |
| Reference:
|
[8] Urbański, P.: Double vector bundles in classical mechanics.Rend. Sem. Mat. Torino (1997). MR 1618142 |
| Reference:
|
[9] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles.Marcel Dekker, Inc., New York, 1973. MR 0350650 |
| . |
