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Principal bundle structure on jet prolongations of frame bundles

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Mathematica Slovaca

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 r n . For a structure group of J r FX we find a suitable subgroup of G r n . 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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Authors and Affiliations

  1. Department of Physics, Mathematics and Techniques, University of Prešov, Ul. 17. novembra 1, SK-081 16, Prešov, Slovakia

    J. Brajerčík

  2. School of Mathematics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian zone, Beijing, 100081, China

    M. Demko & D. Krupka

  3. Department of Mathematics, La Trobe University, Melbourne, Victoria, 3086, Australia

    M. Demko & D. Krupka

  4. Department of Mathematics, University of Ostrava, 30. dubna 22, CZ-701 03, Ostrava, Czech Republic

    M. Demko & D. Krupka

Authors
  1. J. Brajerčík
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  2. M. Demko
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  3. D. Krupka
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Corresponding author

Correspondence to J. Brajerčík.

Additional information

Communicated by Július Korbaš

The first and third authors acknowledge support of the National Science Foundation of China (Grant No. 10932002) and of the Czech Science Foundation (Grant 201/09/0981). This research was also supported by the Slovak Research and Development Agency (Grant MVTS SK-CZ-0006-09) and by the Ministry of Education, Youth and Sports (Grant KONTAKT MEB0810005). The first two authors are also grateful to the Ministry of Education of the Slovak Republic (Grant VEGA 1/0577/10). The first author was also supported by the University of Prešov, Slovakia, and its Faculty of Humanities and Natural Sciences.

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Brajerčík, J., Demko, M. & Krupka, D. Principal bundle structure on jet prolongations of frame bundles. Math. Slovaca 64, 1277–1290 (2014). https://doi.org/10.2478/s12175-014-0275-x

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  • DOI: https://doi.org/10.2478/s12175-014-0275-x

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