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Equivalence of paths in Galilean geometry. (English. Russian original) Zbl 1454.53015

J. Math. Sci., New York 245, No. 3, 297-310 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 144, 3-16 (2018).
Summary: 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.

MSC:

53A40 Other special differential geometries
53A55 Differential invariants (local theory), geometric objects
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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