Geodesic
Classification of principal connections naturally induced on $W^2PE$
Archivum mathematicum, Tome 44 (2008) no. 5, pp. 535-547 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $.
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 $.
Classification : 53C05, 53C10, 58A20, 58A32
Keywords: natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection 
@article{ARM_2008_44_5_a13,
     author = {Vondra, Jan},
     title = {Classification of principal connections naturally induced on $W^2PE$},
     journal = {Archivum mathematicum},
     pages = {535--547},
     year = {2008},
     volume = {44},
     number = {5},
     mrnumber = {2501583},
     zbl = {1212.53040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008_44_5_a13/}
}
TY  - JOUR
AU  - Vondra, Jan
TI  - Classification of principal connections naturally induced on $W^2PE$
JO  - Archivum mathematicum
PY  - 2008
SP  - 535
EP  - 547
VL  - 44
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ARM_2008_44_5_a13/
LA  - en
ID  - ARM_2008_44_5_a13
ER  - 
%0 Journal Article
%A Vondra, Jan
%T Classification of principal connections naturally induced on $W^2PE$
%J Archivum mathematicum
%D 2008
%P 535-547
%V 44
%N 5
%U http://geodesic.mathdoc.fr/item/ARM_2008_44_5_a13/
%G en
%F ARM_2008_44_5_a13
Vondra, Jan. Classification of principal connections naturally induced on $W^2PE$. Archivum mathematicum, Tome 44 (2008) no. 5, pp. 535-547. http://geodesic.mathdoc.fr/item/ARM_2008_44_5_a13/

[1] Doupovec, M., Mikulski, W. M.: Reduction theorems for principal and classical connections. to appear.

[2] Doupovec, M., Mikulski, W. M.: Holonomic extensions of connections and symmetrization of jets. Rep. Math. Phys. 60 (2007), 299–316. | DOI | MR

[3] Eck, D. J.: Gauge-natural bundles and generalized gauge theories. Mem. Amer. Math. Soc. 247 (1981), 48p. | MR | Zbl

[4] Fatibene, L., Francaviglia, M.: Natural and Gauge Natural Formalism for Classical Field Theories. Kluwer Academic Publishers, Dordrecht-Boston-London, 2003. | MR | Zbl

[5] Janyška, J.: On the curvature of tensor product connections and covariant differentials. Rend. Circ. Mat. Palermo (2) Suppl. 72 (2004), 135–143. | MR | Zbl

[6] Janyška, J.: Reduction theorems for general linear connections. Differential Geom. Appl. 20 (2004), 177–196. | DOI | MR | Zbl

[7] Janyška, J.: Higher order valued reduction theorems for classical connections. Cent. Eur. J. Math. 3 (2005), 294–308. | DOI | MR | Zbl

[8] Kolář, I.: Some natural operators in differential geometry. Differential Geom. Appl., D. Reidel, 1987, pp. 91–110. | MR

[9] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Springer–Verlag, 1993. | MR

[10] Kolář, I., Virsik, G.: Connections in first principal prolongations. Rend. Circ. Mat. Palermo (2) Suppl. 43 (1996), 163–171. | MR

[11] Krupka, D., Janyška, J.: Lectures on Differential Invariants. Folia Fac. Sci. Natur. Univ. Purkynian. Brun. Math., 1990. | MR

[12] Nijenhuis, A.: Natural bundles and their general properties. Differential Geom. (1972), 317–334, In honour of K. Yano, Kinokuniya, Tokyo. | MR | Zbl

[13] Terng, C. L.: Natural vector bundles and natural differential operators. Amer. J. Math. 100 (1978), 775–823. | DOI | MR | Zbl