On Frenet Framme of Null Curves in Three Dimensional Minkowski Spaces

This article investigates the Frenet frame of null curves which are embedded inside three-dimensional Minkowski spacetime M^2,1, a significant topic of differential geometry and Lorentzian geometry. Unlike Euclidean geometry, the indefinite metric of Minkowski space introduces unique challenges and properties. We analyse the Frenet frame components, including the tangent of curves, and normal which is orthogonal, and binormal this is a perpendicular to both vectors, and derive the associated Frenet-Serret equations. Additionally, we propose new formulations for these equations specific to null curves in the Minkowski space. A practical example is visualized using Maple to illustrate the theoretical results. This study contributes to the deeper understanding of the geometric behaviour of null curves in Lorentzian settings.