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Principal bundle structure on jet prolongations of frame bundles |
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| Authors: | J Brajerčík M Demko D Krupka |
| Institution: | 1. Department of Physics, Mathematics and Techniques, University of Pre?ov, Ul. 17. novembra 1, SK-081 16, Pre?ov, Slovakia 2. School of Mathematics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian zone, Beijing, 100081, China 3. Department of Mathematics, La Trobe University, Melbourne, Victoria, 3086, Australia 4. Department of Mathematics, University of Ostrava, 30. dubna 22, CZ-701 03, Ostrava, Czech Republic |
| Abstract: | In this paper, we introduce the structure of a principal bundle on the r-jet prolongation J r FX of the frame bundle FX over a manifold X. Our construction reduces the well-known principal prolongation W r FX of FX with structure group G n r . For a structure group of J r FX we find a suitable subgroup of G n r . We also discuss the structure of the associated bundles. We show that the associated action of the structure group of J r FX corresponds with the standard actions of differential groups on tensor spaces. |
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