Geometric analysis of slant timelike-ruled surfaces and Bertrand offsets in Minkowski 3-space

This study investigates the geometric properties of slant timelike-ruled surfaces and their Bertrand offsets in Minkowski space. By deriving their parametric equations, we examine the structural characteristics of these surfaces and classify their offset relationships. Through the use of geodesic curvatures, we establish conditions for parallel Bertrand offsets and analyze their compatibility with the Blaschke frame. Explicit representations of the slant timelike-ruled surface and its Bertrand offset are formulated, with specific parameter values chosen to explore their geometric behavior. The influence of these parameters on surface geometry is demonstrated through graphical models. These results advance the understanding of ruled surface theory in Lorentzian geometry and offer valuable insights into applications in mathematical physics and differential geometry.