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A Note on Jet and Geometric Approach to Higher Order Connections

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Algebra, Geometry and Mathematical Physics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 85))

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Abstract

We compare two ways of interpreting higher order connections. The geometric approach lies in the decomposition of higher order tangent space into the horizontal and vertical structures while the jet-like approach considers a higher order connection as the section of a jet prolongation of a fibered manifold. Particularly, we use the Ehresmann prolongation of a general connection and study the result from the point of view of geometric theory. We pay attention to linear connections, too.

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Acknowledgments

The first author was supported by the grant of Tartu University TMTMM 0039, the second author by the project NETME CENTRE PLUS (LO1202). The results of the project NETME CENTRE PLUS (LO1202) were co-funded by the Ministry of Education, Youth and Sports within the support programme “National Sustainability Programme I”.

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Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, J.Liivi 2, 50409, Tartu, Estonia

    Maïdo Rahula

  2. Faculty of Mechanical Engineering, Institute of Mathematics, Brno University of Technology, Technická 2, 61669, Brno, Czech Republic

    Petr Vašík

Authors
  1. Maïdo Rahula
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  2. Petr Vašík
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Corresponding author

Correspondence to Maïdo Rahula .

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Editors and Affiliations

  1. Informatique et Applications, Université of Haute Alsace, Laboratoire de Mathématiques, Mulhouse, France

    Abdenacer Makhlouf

  2. Tallinn University of Technology, Dept. Mathematics, Tallinn, Estonia

    Eugen Paal

  3. Culture and Communication (UKK) Division of Applied Mathematics, Mälardalen University, The School of Education, Västerås, Sweden

    Sergei D. Silvestrov

  4. Dept. Mathematical Sciences, University of Göteborg, Göteborg, Sweden

    Alexander Stolin

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Rahula, M., Vašík, P. (2014). A Note on Jet and Geometric Approach to Higher Order Connections. In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A. (eds) Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55361-5_24

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