# On the iterated absolute differentiation on some functional bundles

Archivum Mathematicum (1997)

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

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topCabras, 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 -

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