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Foundations of singular Finsler geometry

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Abstract

We present an approach leading to Finsler geometry without differential calculus of tensors. Several natural examples of such singular Finsler spaces are studied. One class of such examples contains Busemann G-spaces with non-positive curvature. Starting with a singular version of the axiomatics, some simplest properties known in the smooth Finsler geometry are interpreted.

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Acknowledgements

I am very grateful to Athanase Papadopoulos for his invaluable help in preparing this paper. My thanks to the referee for a number of important remarks.

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Authors and Affiliations

  1. Northern (Arctic) Federal University named after M.V. Lomonosov, Severnaya Dvina Emb., 17, 163002, Arkhangelsk, Russia

    Pavel Andreev

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  1. Pavel Andreev
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Correspondence to Pavel Andreev.

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Supported by RFBR, Grant 14-01-00219.

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Andreev, P. Foundations of singular Finsler geometry. European Journal of Mathematics 3, 767–787 (2017). https://doi.org/10.1007/s40879-017-0169-x

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  • DOI: https://doi.org/10.1007/s40879-017-0169-x

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