| Title:
|
Prolongation of tangent valued forms to Weil bundles (English) |
| Author:
|
Cabras, Antonella |
| Author:
|
Kolář, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
139-145 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the so-called complete lifting of tangent valued forms from a manifold $M$ to an arbitrary Weil bundle over $M$ preserves the Frölicher-Nijenhuis bracket. We also deduce that the complete lifts of connections are torsion-free in the sense of M. Modugno and the second author. (English) |
| Keyword:
|
Weil bundle |
| Keyword:
|
tangent valued form |
| Keyword:
|
Frölicher-Nijenhuis bracket |
| Keyword:
|
complete lift |
| Keyword:
|
connection |
| Keyword:
|
torsion |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0843.53021 |
| idMR:
|
MR1357981 |
| . |
| Date available:
|
2008-06-06T21:28:31Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107533 |
| . |
| Reference:
|
[1] Gancarzewicz, J.: Complete lifts of tensor fields of type $(1, k)$ to natural bundles.Zeszyty Nauk. UJ, Krak¢w 23 (1982), 43–79. Zbl 0547.55014, MR 0670571 |
| Reference:
|
[2] Gancarzewicz, J., Mikulski, W., Pogoda, Z.: Lifts of some tensor fields and connections to product preserving functors.to appear in Nagoya Math. J. MR 1295815 |
| Reference:
|
[3] Kol ©, I.: Covariant approach to natural transformations of Weil functors.Comment. Math. Univ. Carolinae 27 (1986), 723–729. MR 0874666 |
| Reference:
|
[4] Kol ©, I., Michor, P. W., Slov k, J.: Natural operations in differential geometry.Springer-Verlag 1993. MR 1202431 |
| Reference:
|
[5] Kol ©, I. Modugno, M.: Torsions of connections on some natural bundles.Differential Geometry and Its Applications 2 (1992), 1–16. MR 1244453 |
| Reference:
|
[6] Mangiarotti, L. Modugno. M.: Graded Lie algebras and connections on a fibred space.Journ. Math. Pures and Appl. 83 (1984), 111–120. MR 0776913 |
| Reference:
|
[7] Morimoto, A.: Prolongations of connections to bundles of infinitely near points.J. Diff. Geo. 11 (1976), 479–498. MR 0445422 |
| Reference:
|
[8] Slov k, J.: Prolongations of connections and sprays with respect to Weil functors.Suppl. Rendiconti Circolo Mat. Palermo, Serie II 14 (1987), 143–155. MR 0920852 |
| Reference:
|
[9] Weil, A.: Théorie des pointes proches sur les variétés différentielles.Colloque de topologie et géométrie différentielle, Strasbourg (1953), 111–117. MR 0061455 |
| . |
