Magnetic Curves in Differential Geometry: A Comprehensive Survey

The concept of “magnetic lines of force,” or “magnetic curves”, was introduced in the 1830s by Michael Faraday (1791–1867); his work provided the foundation for the modern understanding of magnetic fields. In differential geometry, a magnetic curve is a concept that arises from the intersection of geometry and physics. These curves represent the trajectories of a charged particle experiencing the Lorentz force as it travels through a magnetic field. These curves have garnered significant interest due to their intricate geometric properties and diverse applications. This paper provides a comprehensive exploration of magnetic curves, delving into their fundamental characteristics and classification.