Fixed-axis spacelike ruled surfaces and their evolute offsets

Abstract

This study investigates fixed-axis spacelike ruled surfaces and their evolute offset counterparts within E13 (Minkowski 3-space). The analysis utilizes the Blaschke frame associated with the striction curves of these surfaces. Spacelike ruled surfaces play a crucial role in various fields of both classical and modern physics. The research begins by introducing the fundamental concepts of fixed-axis spacelike ruled surfaces and defining a height function that establishes the necessary criteria for a ruled surface to be classified as a fixed-axis spacelike ruled surface. Subsequently, the study derives parameterization for both the fixed-axis spacelike ruled surfaces and their evolute offsets. Finally, several surface models are extended and visually represented through graphical illustrations.