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arXiv · 2510.00170

Notes on the Geometry of Electromagnetic Fields and Maxwell's Equations along a non-null curves in non flat-3D space forms $M_{q}^{3}(c)$

Fatma Almaz·Cumali Ekici
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Abstract

In this paper, the directional derivatives in accordance with the orthonormal frame {T, N, B} are defined in $M_{q}^{3}(c)$, 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 $M_{q}^{3}(c)$ according to curve $\alpha (s,\xi ,\eta )$ 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 $M_{q}^{3}(c).$

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Fatma Almaz, Cumali Ekici. 2025-09-30. Notes on the Geometry of Electromagnetic Fields and Maxwell's Equations along a non-null curves in non flat-3D space forms $M_{q}^{3}(c)$. https://arxiv.org/abs/2510.00170

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