![]() It is possible to circumvent this limitation by moving from the complete Maxwell’s equations to the approximation of geometric optics. ![]() ![]() In the Riemannian geometrization of Maxwell’s equations, the requirement of a single impedance of the medium is critical. Practically all the considered types of electromagnetic media require less than ten parameters to describe the constitutive tensor. The structure of the dielectric and magnetic permittivity is written out for them, the number of significant components for these tensors is determined. ![]() To determine the applicability of Riemannian geometrization, the most common variants of electromagnetic media are considered. To determine whether the lack of components is really critical for the application of Riemannian geometrization. It is necessary to study the scope of applicability of the Riemannian geometrization of Maxwell’s equations. It is assumed that this discrepancy prevents the application of Riemannian geometrization of Maxwell’s equations. With Riemannian geometrization, the constitutive tensor is constructed from a Riemannian metric tensor having 10 components. In the classical description of the equations of electrodynamics in the medium, a constitutive tensor with 20 components is used. 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.
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