We deduce further properties of connections on the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base, which we introduced in [2]. In particular, we define the vertical prolongation of such a connection, discuss the iterated absolute differentiation by means of an auxiliary linear connection on the base manifold and prove the general Ricci identity.
@article{107594,
author = {Antonella Cabras and Ivan Kol\'a\v r},
title = {On the iterated absolute differentiation on some functional bundles},
journal = {Archivum Mathematicum},
volume = {033},
year = {1997},
pages = {23-35},
zbl = {0910.53014},
mrnumber = {1464298},
language = {en},
url = {http://dml.mathdoc.fr/item/107594}
}
Cabras, Antonella; Kolář, Ivan. On the iterated absolute differentiation on some functional bundles. Archivum Mathematicum, Tome 033 (1997) pp. 23-35. http://gdmltest.u-ga.fr/item/107594/
The Ricci identity for general connections, Proceedings Conf. Diff. Geom. and Applications, 1995, Masaryk University, Brno 1996, 121-126. | MR 1406331 | Zbl 0862.53023
Connections on some functional bundles, Czechoslovak Math. J., 45(1995), 529-548. | MR 1344519
The universal connection of an arbitrary system, to appear in Annali di Matematica. | MR 1746921
Extension du calcul des jets aux jets non holonomes, CRAS Paris, 239 (1954), 1762-1764. | MR 0066734 | Zbl 0057.15603
Smooth structures, Category theory 1981, LNM 962, Springer-Verlag, 1982, 69-81. | MR 0682945
Galilei general relativistic quantum mechanics, to appear.
Connections in 2-fibred manifolds, Arch. Math.(Brno), XVII(1981), 23-30. | MR 0672485
Higher order absolute differentiation with respect to generalized connections, Differential Geometry, Banach Center Publications, Volume 12, Warszaw 1984, 153-162. | MR 0961078
An infinite dimensional motivation in higher order geometry, Proceedings Conf. Diff. Geom. and Applications, 1995, Masaryk University, Brno 1996, 151-159. | MR 1406335
Natural operations in differential geometry, Springer-Verlag, 1993. | MR 1202431
Connections and differential calculus on fibered manifolds, preprint.
New results on the theory of connections: systems, overconnections and prolongations, Differential Geometry and Its Applications, Proceedings, D. Reidel Publishing Company, 1987, 243-269. | MR 0923352 | Zbl 0636.53039
Représentation des jets non holonomes par des morphisms vectoriels doubles soudés, CRAS Paris, série A 278, 1974, 1523-1526. | MR 0388432
Smooth structures on fibre jet spaces, Czechoslovak Math. J., 36(1986), 358-375. | MR 0847766
Total connections in Lie groupoids, Arch. Math.(Brno), 31(1995), 183-200. | MR 1368257 | Zbl 0841.53024