Geodesic
Natural transformations of connections on the first principal prolongation
Archivum mathematicum, Tome 50 (2014) no. 1, pp. 21-25 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2014-1-21
Classification : 53C05, 58A32
Keywords: natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection 
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Vondra, Jan. Natural transformations of connections on the first principal prolongation. Archivum mathematicum, Tome 50 (2014) no. 1, pp. 21-25. doi: 10.5817/AM2014-1-21

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

[2] Janyška, J.: Reduction theorems for general linear connections. Differential Geom. Appl. 20 (2) (2004), 177–196. | DOI | MR | Zbl

[3] Janyška, J.: Higher order Utiyama invariant interaction. Rep. Math. Phys. 59 (1) (2007), 63–81. | DOI | MR

[4] Janyška, J., Vondra, J.: Natural principal connections on the principal gauge prolongation of a principal bundle. Rep. Math. Phys. 64 (3) (2009), 395–415. | DOI | MR | Zbl

[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. | MR

[6] Kolář, I.: Connections on higher order frame bundles and their gauge analogies. Variations, Geometry and Physics, Nova Science Publishers, 2008, pp. 199–223. | MR

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

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

[9] Vondra, J.: Classification of principal connections naturally induced on $W^2PE$. Arch. Math. (Brno) 44 (5) (2008), 535–547. | MR | Zbl

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