Geodesic
Equivalence of Paths in Galilean Geometry
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 3-16.

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An explicit description of finite transcendence bases in differential fields of differential rational functions that are invariant under the action of Galilean transformation group in a real finite-dimensional space is presented. Necessary and sufficient conditions of the equivalence of paths in the $n$-dimensional Galilean space are obtained.
Keywords: Galilean space, differential invariant, transcendence basis, path in a finite-dimensional space. 
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V. I. Chilin; K. K. Muminov. Equivalence of Paths in Galilean Geometry. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 3-16. http://geodesic.mathdoc.fr/item/INTO_2018_144_a0/

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