Geometrical information coded in Maxwell’s equations: a review

The purpose of this paper is to show how the geometrical information of Maxwell's equations is coded into the constitutive equations. The Maxwell's equations have been written with the tensorial algebra into a three-dimensional Euclidean space and compared with the usual four-dimensional relativistic approach. This simple geometry allows the finding of the relativistic information coded on the electric and magnetic fields, showing that they are not independent as relativity affirm obtaining their transformation for a moving inertial observer. The main value of the paper is to present a simple mathematical tool which enables the engineers or applied physicists to obtain the relativistic transformations of the fields without using four-dimensional geometries and the more sophisticated mathematical techniques.

keywords: Differential equations, Differential geometry, Electromagnetism