Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)3301210.22363/2658-4670-2022-30-4-305-317Research ArticleConstitutive tensor in the geometrized Maxwell theoryKorolkovaAnna V.<p>Docent, Candidate of Sciences in Physics and Mathematics, Associate Professor of Department of Applied Probability and Informatics</p>korolkova-av@rudn.ruhttps://orcid.org/0000-0001-7141-7610Peoples’ Friendship University of Russia (RUDN University)2612202230430531726122022Copyright © 2022, Korolkova A.V.2022<p style="text-align: justify;">It is generally accepted that the main obstacle to the application of Riemannian geometrization of Maxwell’s equations is an insufficient number of parameters defining a geometrized medium. In the classical description of the equations of electrodynamics in the medium, a constitutive tensor with 20 components is used. With Riemannian geometrization, the constitutive tensor is constructed from a Riemannian metric tensor having 10 components. It is assumed that this discrepancy prevents the application of Riemannian geometrization of Maxwell’s equations. It is necessary to study the scope of applicability of the Riemannian geometrization of Maxwell’s equations. To determine whether the lack of components is really critical for the application of Riemannian geometrization. To determine the applicability of Riemannian geometrization, the most common variants of electromagnetic media are considered. The structure of the dielectric and magnetic permittivity is written out for them, the number of significant components for these tensors is determined. Practically all the considered types of electromagnetic media require less than ten parameters to describe the constitutive tensor. In the Riemannian geometrization of Maxwell’s equations, the requirement of a single impedance of the medium is critical. It is possible to circumvent this limitation by moving from the complete Maxwell’s equations to the approximation of geometric optics. The Riemannian geometrization of Maxwell’s equations is applicable to a wide variety of media types, but only for approximating geometric optics.</p>geometrization of Maxwell’s equationspermeability tensordielectric constantmagnetic permeabilitygeometric opticsгеометризация уравнений Максвеллатензор проницаемостейдиэлектрическая проницаемостьмагнитная проницаемостьгеометрическая оптика[F. C. Klein, “Ueber die sogenannte Nicht-Euklidische Geometrie,” German, in Gau und die Anfnge der nicht-euklidischen Geometrie, ser. Teubner-Archiv zur Mathematik, vol. 4, Wien: Springer-Verlag Wien, 1985, pp. 224-238. 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