Investigating Spacelike Polynomial Curves in Minkowski 3-Space Using a Frenet-Like Curve Fram

This study investigates the properties of spacelike polynomial curves in Minkowski 3- space using an innovative framework known as the Frenet-like curve frame (Flc-frame). Traditional methods, such as the Frenet frame, depend on the first and second derivatives of a curve, which can be limiting for polynomial curves where higher-order derivatives lack geometric clarity. The Flc-frame addresses these limitations by leveraging intrinsic curve properties to derive Flc-formulae and curvatures, establishing their interrelationships. A concrete example demonstrates the efficacy of the Flc-frame in characterizing such curves. Additionally, we introduce novel integral curves defined via the Flc-frame and its curvatures, extending this framework to Minkowski 3-space. Our findings reveal that the Flc-frame generalizes the Frenet frame, providing a more adaptable tool for curve analysis, especially in scenarios where traditional methods falter. This research enhances the understanding of polynomial curves in Minkowski space and lays the groundwork for future studies on integral curves and their geometric properties.