It is proven that the differential equation for the null-curves of the pseudo-Euclidean space ℝ2,n defines a flat dynamical system in the sense of optimal control theory. The connection with general gauge theories is briefly discussed.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 76–80, July, 2015.
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Latyshev, A.M., Lyakhovich, S.L. & Sharapov, A.A. Null-Curves in ℝ2,n as Flat Dynamical Systems. Russ Phys J 58, 959–964 (2015). https://doi.org/10.1007/s11182-015-0595-5
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DOI: https://doi.org/10.1007/s11182-015-0595-5