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

Research Abstract

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.

Research Authors
Rashad A. Abdel-Baky
Research Date
Research Department
Research Journal
AIP Advances
Research Year
2025