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Equivalence of Paths in Galilean Geometry

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Abstract

In this paper, we present an explicit description of finite transcendence bases in the differential field of differential rational functions that are invariant under the action of the Galilean transformation group in a real finite-dimensional space. Necessary and sufficient conditions of the equivalence of paths in the n-dimensional Galilean space are obtained.

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Authors and Affiliations

  1. National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan

    V. I. Chilin & K. K. Muminov

Authors
  1. V. I. Chilin
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  2. K. K. Muminov
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Correspondence to V. I. Chilin.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 144, Proceedings of the Conference “Problems of Modern Topology and Its Applications” (May 11–12, 2017), Tashkent, Uzbekistan, 2018.

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Chilin, V.I., Muminov, K.K. Equivalence of Paths in Galilean Geometry. J Math Sci 245, 297–310 (2020). https://doi.org/10.1007/s10958-020-04691-7

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