A Study of Timelike Spherical Trajectories via the Equiform Bishop Approach in 3D Minkowski Space

Abstract

This article develops the equiform variant of Bishop’s moving frame for timelike regular curves embedded in three-dimensional Minkowski space. Within this framework we propose a definition of equiform timelike spherical curves determined by the equiform Bishop frame and derive a sharp criterion—both necessary and sufficient—that characterizes when a timelike equiform curve lies on an equiform sphere. In addition, several classification results are obtained for equiform spherical trajectories whose equiform principal normal vector is spacelike. Examples of structural relations between equiform curvature functions and sphericality are presented and discussed.