Second order connections on some functional bundles

Antonella Cabras; Ivan Kolář

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 4, page 347-365
  • ISSN: 0044-8753

Abstract

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We study the second order connections in the sense of C. Ehresmann. On a fibered manifold Y , such a connection is a section from Y into the second non-holonomic jet prolongation of Y . Our main aim is to extend the classical theory to the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. This requires several new geometric results about the second order connections on Y , which are deduced in the first part of the paper.

How to cite

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Cabras, Antonella, and Kolář, Ivan. "Second order connections on some functional bundles." Archivum Mathematicum 035.4 (1999): 347-365. <http://eudml.org/doc/248368>.

@article{Cabras1999,
abstract = {We study the second order connections in the sense of C. Ehresmann. On a fibered manifold $Y$, such a connection is a section from $Y$ into the second non-holonomic jet prolongation of $Y$. Our main aim is to extend the classical theory to the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. This requires several new geometric results about the second order connections on $Y$, which are deduced in the first part of the paper.},
author = {Cabras, Antonella, Kolář, Ivan},
journal = {Archivum Mathematicum},
keywords = {second order connection; non-holonomic 2-jet; absolute differentiation; bundle of smooth maps; connection on a functional bundle; second order connection; non-holonomic 2-jet; absolute differentiation; bundle of smooth maps; connection on a functional bundle},
language = {eng},
number = {4},
pages = {347-365},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Second order connections on some functional bundles},
url = {http://eudml.org/doc/248368},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Cabras, Antonella
AU - Kolář, Ivan
TI - Second order connections on some functional bundles
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 4
SP - 347
EP - 365
AB - We study the second order connections in the sense of C. Ehresmann. On a fibered manifold $Y$, such a connection is a section from $Y$ into the second non-holonomic jet prolongation of $Y$. Our main aim is to extend the classical theory to the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. This requires several new geometric results about the second order connections on $Y$, which are deduced in the first part of the paper.
LA - eng
KW - second order connection; non-holonomic 2-jet; absolute differentiation; bundle of smooth maps; connection on a functional bundle; second order connection; non-holonomic 2-jet; absolute differentiation; bundle of smooth maps; connection on a functional bundle
UR - http://eudml.org/doc/248368
ER -

References

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