A new frame for non-lightlike curves in Minkowski 3-space: hybrid frame

Abstract

In this study, we introduce a hybrid frame consisting of elliptic, hyperbolic, and parabolic vectors for the study of non-lightlike curves in Minkowski 3-space. In contrast to classical approaches that treat different causal characters separately, the proposed frame allows these vector types to be considered within a single framework. We define the curvature and torsion functions with respect to the hybrid frame and examine their relations to the corresponding Frenet invariants. In addition, we investigate the osculating spheres of non-lightlike curves using this frame and obtain characterizations of their centers. The results provide an alternative formulation for the geometric analysis of non-lightlike curves and contribute to the existing theory of curves in Minkowski space.