Differential invariants of curves in Galilean geometry
Vladimir ChilinNational University of Uzbekistan named after M.Ulugbek, University str. 4, Tashkent 100174, UzbekistanK. K. MuminovNational University of Uzbekistan named after M.Ulugbek, University str. 4, Tashkent 100174, Uzbekistan
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Annotatsiya
Let Γn be an n-dimensional Galilean space over the field ℝ of real numbers, let Γ(n, ℝ) be the Galilean group of linear transformations in Γn and let ℝn ⨞Γ(n, ℝ) be the semidirect product of the groups ℝn and Γ(n, ℝ). We introduce the special invariant parametrization for curves α ⊂ Γ(n, ℝ), and using this parametrization we obtain criterion for the G-equivalence of curves α and β (i.e. β = g(α) for some g ∈ G) with respect to the action of groups Γ(n, ℝ) and ℝn ⨞Γ(n, ℝ).
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