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

top
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

top

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

top
  1. Prolongation of tangent valued forms to Weil bundles, Arch. Math. (Brno) 31 (1995), 139–145. MR1357981
  2. On the second order absolute differentiation, Suppl. Rendiconti Circolo Mat. Palermo, Serie II 59 (1999), 123–133. MR1692263
  3. Second order connections on some functional bundles, Arch. Math. (Brno) 35 (1999), 347–365. MR1744522
  4. Prolongation of projectable tangent valued forms, to appear in Rendiconti Palermo. MR1942654
  5. Iteration of fiber product preerving bundle functors, to appear. MR1872045
  6. Extension du calcul des jets aux jets non holonomes, CRAS Paris 239 (1954), 1762–1764. Zbl0057.15603MR0066734
  7. Sur les connexions d’ordre supérieur, Atti del V Cong. dell’Unione Mat. Italiana, 1955, Roma Cremonese 1956, 344–346. 
  8. The Hamilton formalism in the calculus of variations, Ann. Inst. Fourier (Grenoble) 23 (1973), 203–267. MR0341531
  9. Higher order absolute differentiation with respect to generalized connections, Differential Geometry, Banach Center Publications 12 (1984), 153–162. MR0961078
  10. An infinite dimensional motivation in higher order geometry, Proc. Conf. Diff. Geom. and Applications 1995, Masaryk University, Brno 1996, 151–159. MR1406335
  11. Natural Operations in Differential Geometry, Springer--Verlag, 1993. MR1202431
  12. Natural lifting of connections to vertical bundles, Suppl. Rendiconti Circolo Mat. Palermo, Serie II 63 (2000), 97–102. MR1758084
  13. Introduction to the theory of semi-holonomic jets, Arch. Math. (Brno) 33 (1997), 173–189. Zbl0915.58004MR1478771
  14. Graded Lie algebras and connections on a fibered space, Journ. Math. Pures et Appl. 83 (1984), 111–120. MR0776913
  15. Représentation des jets non holonomes par les morphisms vectoriels doubles soudés, CRAS Paris, série A278 (1974), 1523–1526. MR0388432
  16. On quasijet bundles, to appear in Rendiconti Palermo. MR1764094
  17. On the holonomity of higher order connections, Cahiers Topol. Géom. Diff. 12 (1971), 197–212. Zbl0223.53026MR0305294
  18. Théorie des points proches sur les variétés différentielles, Colloque de topol. et géom. diff., Strasbourg (1953), 111-117. MR0061455

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.