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Keywords:
natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection
natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection
Summary:
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.
References:
[1] Fatibene, L., Francaviglia, M.: Natural and Gauge Natural Formalism for Classical Field Theories. Kluwer Academic Publishers, Dordrecht/Boston/London, 2003. MR 2039451 | Zbl 1138.81303
[2] Janyška, J.: Reduction theorems for general linear connections. Differential Geom. Appl. 20 (2) (2004), 177–196. DOI 10.1016/j.difgeo.2003.10.006 | MR 2038554 | Zbl 1108.53016
[3] Janyška, J.: Higher order Utiyama invariant interaction. Rep. Math. Phys. 59 (1) (2007), 63–81. DOI 10.1016/S0034-4877(07)80005-X | MR 2308635
[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 10.1016/S0034-4877(10)00002-9 | MR 2602937 | Zbl 1195.53040
[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 0923346
[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 2523439
[7] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry. Springer–Verlag, 1993. MR 1202431
[8] Krupka, D., Janyška, J.: Lectures on Differential Invariants. Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., Brno, 1990. MR 1108622
[9] Vondra, J.: Classification of principal connections naturally induced on $W^2PE$. Arch. Math. (Brno) 44 (5) (2008), 535–547. MR 2501583 | Zbl 1212.53040
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