Natural transformations of connections on the first principal prolongation

Jan Vondra

Archivum Mathematicum (2014)

  • Volume: 050, Issue: 1, page 21-25
  • ISSN: 0044-8753

Abstract

top
We consider a vector bundle E M and the principal bundle P E of frames of E . We determine all natural transformations of the connection bundle of the first order principal prolongation of principal bundle P E into itself.

How to cite

top

Vondra, Jan. "Natural transformations of connections on the first principal prolongation." Archivum Mathematicum 050.1 (2014): 21-25. <http://eudml.org/doc/261063>.

@article{Vondra2014,
abstract = {We consider a vector bundle $E\rightarrow M$ and the principal bundle $PE$ of frames of $E$. We determine all natural transformations of the connection bundle of the first order principal prolongation of principal bundle $PE$ into itself.},
author = {Vondra, Jan},
journal = {Archivum Mathematicum},
keywords = {natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection; natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection},
language = {eng},
number = {1},
pages = {21-25},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Natural transformations of connections on the first principal prolongation},
url = {http://eudml.org/doc/261063},
volume = {050},
year = {2014},
}

TY - JOUR
AU - Vondra, Jan
TI - Natural transformations of connections on the first principal prolongation
JO - Archivum Mathematicum
PY - 2014
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 050
IS - 1
SP - 21
EP - 25
AB - We consider a vector bundle $E\rightarrow M$ and the principal bundle $PE$ of frames of $E$. We determine all natural transformations of the connection bundle of the first order principal prolongation of principal bundle $PE$ into itself.
LA - eng
KW - natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection; natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection
UR - http://eudml.org/doc/261063
ER -

References

top
  1. Fatibene, L., Francaviglia, M., Natural and Gauge Natural Formalism for Classical Field Theories, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003. (2003) Zbl1138.81303MR2039451
  2. Janyška, J., 10.1016/j.difgeo.2003.10.006, Differential Geom. Appl. 20 (2) (2004), 177–196. (2004) Zbl1108.53016MR2038554DOI10.1016/j.difgeo.2003.10.006
  3. Janyška, J., 10.1016/S0034-4877(07)80005-X, Rep. Math. Phys. 59 (1) (2007), 63–81. (2007) MR2308635DOI10.1016/S0034-4877(07)80005-X
  4. Janyška, J., Vondra, J., 10.1016/S0034-4877(10)00002-9, Rep. Math. Phys. 64 (3) (2009), 395–415. (2009) Zbl1195.53040MR2602937DOI10.1016/S0034-4877(10)00002-9
  5. Kolář, I., Some natural operators in differential geometry, Differential Geometry and Its Aplications (Brno, 1986), Math. Appl. (East European Ser.), Reidel, Dordrecht, 1987, pp. 91–110. (1987) MR0923346
  6. Kolář, I., Connections on higher order frame bundles and their gauge analogies, Variations, Geometry and Physics, Nova Science Publishers, 2008, pp. 199–223. (2008) MR2523439
  7. Kolář, I., Michor, P.W., Slovák, J., Natural Operations in Differential Geometry, Springer–Verlag, 1993. (1993) MR1202431
  8. Krupka, D., Janyška, J., Lectures on Differential Invariants, Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., Brno, 1990. (1990) MR1108622
  9. Vondra, J., Classification of principal connections naturally induced on W 2 P E , Arch. Math. (Brno) 44 (5) (2008), 535–547. (2008) Zbl1212.53040MR2501583

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.