On the iterated absolute differentiation on some functional bundles

Antonella Cabras; Ivan Kolář

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 1-2, page 23-35
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Cabras, Antonella, and Kolář, Ivan. "On the iterated absolute differentiation on some functional bundles." Archivum Mathematicum 033.1-2 (1997): 23-35. <http://eudml.org/doc/248021>.

@article{Cabras1997,
abstract = {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.},
author = {Cabras, Antonella, Kolář, Ivan},
journal = {Archivum Mathematicum},
keywords = {bundle of smooth maps; connection on a functional bundle; iterated absolute differentiation; iterated 2-jet; Ricci identity; bundle of smooth maps; connection on a functional bundle; iterated absolute differentiation; iterated 2-jet; Ricci identity; nonlinear connection},
language = {eng},
number = {1-2},
pages = {23-35},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the iterated absolute differentiation on some functional bundles},
url = {http://eudml.org/doc/248021},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Cabras, Antonella
AU - Kolář, Ivan
TI - On the iterated absolute differentiation on some functional bundles
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 1-2
SP - 23
EP - 35
AB - 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.
LA - eng
KW - bundle of smooth maps; connection on a functional bundle; iterated absolute differentiation; iterated 2-jet; Ricci identity; bundle of smooth maps; connection on a functional bundle; iterated absolute differentiation; iterated 2-jet; Ricci identity; nonlinear connection
UR - http://eudml.org/doc/248021
ER -

References

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  8. Higher order absolute differentiation with respect to generalized connections, Differential Geometry, Banach Center Publications, Volume 12, Warszaw 1984, 153-162. MR0961078
  9. An infinite dimensional motivation in higher order geometry, Proceedings Conf. Diff. Geom. and Applications, 1995, Masaryk University, Brno 1996, 151-159. MR1406335
  10. Natural operations in differential geometry, Springer-Verlag, 1993. MR1202431
  11. Connections and differential calculus on fibered manifolds, preprint. 
  12. New results on the theory of connections: systems, overconnections and prolongations, Differential Geometry and Its Applications, Proceedings, D. Reidel Publishing Company, 1987, 243-269. Zbl0636.53039MR0923352
  13. Représentation des jets non holonomes par des morphisms vectoriels doubles soudés, CRAS Paris, série A 278, 1974, 1523-1526. MR0388432
  14. Smooth structures on fibre jet spaces, Czechoslovak Math. J., 36(1986), 358-375. MR0847766
  15. Total connections in Lie groupoids, Arch. Math.(Brno), 31(1995), 183-200. Zbl0841.53024MR1368257

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