Prolongation of projectable tangent valued forms
Cabras, Antonella ; Kolář, Ivan
Archivum Mathematicum, Tome 038 (2002), p. 243-257 / Harvested from Czech Digital Mathematics Library

First we deduce some general properties of product preserving bundle functors on the category of fibered manifolds. Then we study the prolongation of projectable tangent valued forms with respect to these functors and describe the complete lift of the Frölicher-Nijenhuis bracket. We also present the coordinate formula for composition of semiholonomic jets.

Publié le : 2002-01-01
Classification:  53C05,  58A20,  58A32
@article{107838,
     author = {Antonella Cabras and Ivan Kol\'a\v r},
     title = {Prolongation of projectable tangent valued forms},
     journal = {Archivum Mathematicum},
     volume = {038},
     year = {2002},
     pages = {243-257},
     zbl = {1090.53031},
     mrnumber = {1942654},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107838}
}
Cabras, Antonella; Kolář, Ivan. Prolongation of projectable tangent valued forms. Archivum Mathematicum, Tome 038 (2002) pp. 243-257. http://gdmltest.u-ga.fr/item/107838/

Prolongation of tangent valued forms to Weil bundles, Arch. Math. (Brno), 31 (1995), 139–145. | MR 1357981

On the jets of fibered manifold morphisms, Cahiers Topo. Géom. Diff. Catégoriques, XL (1999), 21–30. | MR 1682575

Extension du calcul des jets aux jets non holonomes, CRAS Paris, 239 (1954), 1762–1764. | MR 0066734 | Zbl 0057.15603

Lifts of some tensor fields and connections to product preserving functors, Nagoya Math. J. 135 (1994), 1–41. | MR 1295815

Invariants of velocities and higher order Grassmann bundles, J. Geom. Phys. 24 (1998), 244–264. | MR 1491556

Natural Operations in Differential Geometry, Springer-Verlag, 1993. | MR 1202431

Natural lifting of connections to vertical bundles, Rendiconti del Circolo Matematico di Palermo, Ser. II, Supl. 63 (2000), 97–102. | MR 1758084

Torsion of connections on some natural bundles, Diff. Geom. and its Appl. 2 (1992), 1–16. | MR 1244453

Torsion of connections on tangent bundles of higher order, Supplemento ai Rendiconti Palermo, Série II, No 54 (1997), 65–73. | MR 1662727

Graded Lie algebras and connections on a fibered space, J. Math. pures et appl. 63 (1984), 111–120. | MR 0776913

Product preserving bundle functors on fibered manifolds, Archivum Math. (Brno) 32 (1996), 307–316. | MR 1441401 | Zbl 0881.58002

Differential calculus on fibred manifolds, manuscript, 2000. | Zbl 0841.53023

Natural operators transforming projectable vector fields to product preserving bundles, Supplemento ai Rendiconti Palermo, Série II, No 59 (1999), 181–187. | MR 1692269

Théorie des points proches sur les variétés différentielles, Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. | MR 0061455