This analysis defines directional derivatives, modifies Serret-Frenet relations, and solves Maxwell's equations, implying deeper insights into electromagnetic behavior.
In this paper, the directional derivatives in accordance with the orthonormal frame {T, N, B} are defined in Mq³(c), and the extended Serret-Frenet relations by using Frenet formulas are expressed. Furthermore, we express the bending elastic energy function for the same particle in Mq³(c) according to curve $α(s,ξ,η)$ and geometrical interpretation of the energy for unit vector fields and we also solve Maxwell's equations for the electric and magnetic field vectors in Mq³(c).
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Almaz et al. (2025) studied this question.
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