Prolongation of second order connections to vertical Weil bundles

Antonella Cabras; Ivan Kolář

Archivum Mathematicum (2001)

  • Volume: 037, Issue: 4, page 333-347
  • ISSN: 0044-8753

Abstract

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We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra A . In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a B -field for another Weil algebra B and of its A -prolongation.

How to cite

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Cabras, Antonella, and Kolář, Ivan. "Prolongation of second order connections to vertical Weil bundles." Archivum Mathematicum 037.4 (2001): 333-347. <http://eudml.org/doc/248758>.

@article{Cabras2001,
abstract = {We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra $A$. In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a $B$-field for another Weil algebra $B$ and of its $A$-prolongation.},
author = {Cabras, Antonella, Kolář, Ivan},
journal = {Archivum Mathematicum},
keywords = {non-holonomic jet; Weil bundle; Weil field; second order connection; prolongation of connections; non-holonomic jet; Weil bundle; second order connection; prolongation of connection},
language = {eng},
number = {4},
pages = {333-347},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Prolongation of second order connections to vertical Weil bundles},
url = {http://eudml.org/doc/248758},
volume = {037},
year = {2001},
}

TY - JOUR
AU - Cabras, Antonella
AU - Kolář, Ivan
TI - Prolongation of second order connections to vertical Weil bundles
JO - Archivum Mathematicum
PY - 2001
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 037
IS - 4
SP - 333
EP - 347
AB - We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra $A$. In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a $B$-field for another Weil algebra $B$ and of its $A$-prolongation.
LA - eng
KW - non-holonomic jet; Weil bundle; Weil field; second order connection; prolongation of connections; non-holonomic jet; Weil bundle; second order connection; prolongation of connection
UR - http://eudml.org/doc/248758
ER -

References

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  15. Représentation des jets non holonomes par les morphisms vectoriels doubles soudés, CRAS Paris, série A278 (1974), 1523–1526. MR0388432
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