Blaschke frames and the motion of timelike ruled surfaces in Minkowski 3-space

This study explores the geometry of timelike ruled surfaces and their associated Blaschke frames in Minkowski 3-space. It establishes a mapping from spacelike differentiable curves to timelike ruled surfaces and derives the corresponding differential equations governing the Blaschke frame, which encapsulates key geometric vectors of the surface. Central concepts, such as the striction curve and the Disteli-axis, are analyzed, highlighting their roles in the surface’s motion and curvature. The research further investigates the conditions for rotational and translational motions and classifies ruled surfaces based on specific curvature and torsion constraints. Overall, this study offers a comprehensive framework for understanding the geometry and kinematics of timelike ruled surfaces.