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A Unified Approach to the Theory of Connections in Finsler Geometry

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Abstract

We propose a unified approach to the theory of connections in the geometry of sprays and Finsler metrics which, in particular, gives a simple explanation of the well-known fact that all the classical Finslerian connections provide exactly the same formulas appearing in the calculus of variations.

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Notes

  1. We refer to Grifone (1972) for the definition of a symmetric connection.

  2. Here, \([S,\mathscr {J}]\) stands for the Lie derivative of the tensor field \(\mathscr {J}\) along S.

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Acknowledgments

The author would like to thank the support provided by the Mathematischen Instituts der Universität Leipzig, where this work was done, and the financial support provided by the Brazilian program Science Without Borders, Grant No. 232664/2014-5.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Pernambuco, Cidade Universitária, Recife, Pernambuco, Brazil

    Henrique Vitório

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  1. Henrique Vitório
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Correspondence to Henrique Vitório.

Additional information

This work was supported by CNPq, Grant No. 232664/2014-5.

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Vitório, H. A Unified Approach to the Theory of Connections in Finsler Geometry. Bull Braz Math Soc, New Series 48, 317–333 (2017). https://doi.org/10.1007/s00574-016-0014-8

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  • DOI: https://doi.org/10.1007/s00574-016-0014-8

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