Classification of principal connections naturally induced on W 2 P E

Jan Vondra

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 5, page 535-547
  • ISSN: 0044-8753

Abstract

top
We consider a vector bundle E → M and the principal bundle P E of frames of E . Let K be a principal connection on P E and let Λ be a linear connection on M . We classify all principal connections on W 2 P E = P 2 M × M J 2 P E naturally given by K and Λ .

How to cite

top

Vondra, Jan. "Classification of principal connections naturally induced on $W^2PE$." Archivum Mathematicum 044.5 (2008): 535-547. <http://eudml.org/doc/250508>.

@article{Vondra2008,
abstract = {We consider a vector bundle $E\rightarrow M$ and the principal bundle $PE$ of frames of $E$. Let $K$ be a principal connection on $PE$ and let $\Lambda $ be a linear connection on $M$. We classify all principal connections on $W^2PE= P^2M\times _M J^2PE$ naturally given by $K$ and $\Lambda $.},
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 = {5},
pages = {535-547},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Classification of principal connections naturally induced on $W^2PE$},
url = {http://eudml.org/doc/250508},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Vondra, Jan
TI - Classification of principal connections naturally induced on $W^2PE$
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 5
SP - 535
EP - 547
AB - We consider a vector bundle $E\rightarrow M$ and the principal bundle $PE$ of frames of $E$. Let $K$ be a principal connection on $PE$ and let $\Lambda $ be a linear connection on $M$. We classify all principal connections on $W^2PE= P^2M\times _M J^2PE$ naturally given by $K$ and $\Lambda $.
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/250508
ER -

References

top
  1. Doupovec, M., Mikulski, W. M., Reduction theorems for principal and classical connections, to appear. 
  2. Doupovec, M., Mikulski, W. M., 10.1016/S0034-4877(07)80141-8, Rep. Math. Phys. 60 (2007), 299–316. (2007) MR2374824DOI10.1016/S0034-4877(07)80141-8
  3. Eck, D. J., Gauge-natural bundles and generalized gauge theories, Mem. Amer. Math. Soc. 247 (1981), 48p. (1981) Zbl0493.53052MR0632164
  4. Fatibene, L., Francaviglia, M., Natural and Gauge Natural Formalism for Classical Field Theories, Kluwer Academic Publishers, Dordrecht-Boston-London, 2003. (2003) Zbl1138.81303MR2039451
  5. Janyška, J., On the curvature of tensor product connections and covariant differentials, Rend. Circ. Mat. Palermo (2) Suppl. 72 (2004), 135–143. (2004) Zbl1051.53017MR2069401
  6. Janyška, J., 10.1016/j.difgeo.2003.10.006, Differential Geom. Appl. 20 (2004), 177–196. (2004) Zbl1108.53016MR2038554DOI10.1016/j.difgeo.2003.10.006
  7. Janyška, J., 10.2478/BF02479205, Cent. Eur. J. Math. 3 (2005), 294–308. (2005) Zbl1114.53018MR2129910DOI10.2478/BF02479205
  8. Kolář, I., Some natural operators in differential geometry, Differential Geom. Appl., D. Reidel, 1987, pp. 91–110. (1987) MR0923346
  9. Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer–Verlag, 1993. (1993) MR1202431
  10. Kolář, I., Virsik, G., Connections in first principal prolongations, Rend. Circ. Mat. Palermo (2) Suppl. 43 (1996), 163–171. (1996) MR1463518
  11. Krupka, D., Janyška, J., Lectures on Differential Invariants, Folia Fac. Sci. Natur. Univ. Purkynian. Brun. Math., 1990. (1990) MR1108622
  12. Nijenhuis, A., Natural bundles and their general properties, Differential Geom. (1972), 317–334, In honour of K. Yano, Kinokuniya, Tokyo. (1972) Zbl0246.53018MR0380862
  13. Terng, C. L., 10.2307/2373910, Amer. J. Math. 100 (1978), 775–823. (1978) Zbl0422.58001MR0509074DOI10.2307/2373910

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.