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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

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Volume 1, Issue 3


Volume 13 (2015)

On the torsion of linear higher order connections

Ivan Kolář
Published Online: 2003-09-01 | DOI: https://doi.org/10.2478/BF02475215


For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.

Keywords: linear r-th order connection on the tangent bundle; principal connection on the r-th order frame bundle; torsion; integrability of G-structures

Keywords: 53C05; 58A20

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  • [3] I. Kolář: “Torision free connections on higher order frame bundles”, New Developments in Differential Geometry, Proceedings, Kluwer, 1996, pp. 233–241. Google Scholar

  • [4] I. Kolář, P.W. Michor, J. Slovák: Natural Operations in Differential Geometry, Springer-Verlag, 1993, http://www.math.muni.cz/EMIS/monographs/index.html. Google Scholar

  • [5] P.C. Yuen: “Higher order frames and linear connections”, Cahiers Topol. Geom. Diff., Vol. 12, (1971), pp. 333–371. Google Scholar

  • [6] A. Zajtz: Foundations of Differential Geometry of Natural Bundles, Lecture Notes Univ. Caracas, 1984. Google Scholar

About the article

Published Online: 2003-09-01

Published in Print: 2003-09-01

Citation Information: Open Mathematics, Volume 1, Issue 3, Pages 360–366, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02475215.

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© 2003 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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