Physical Interpretations and Geometric Structures of Soliton Behavior in Spacelike Curves Using Anholonomic Coordinates

Abstract

The study focuses on surface motion in three-dimensional Minkowski space, using anholonomic coordinates to analyze unit-speed spacelike curves with timelike normality. It highlights the importance of anholonomic coordinates in investigating important ideas and conclusions based on differential geometry. The study also aims to osculate motion in spacelike curve flows, consider surfaces through the integration of tangent and normal directions using anholonomic coordinates, and investigate their interaction with soliton equations. Building on this foundation, it studies the use of binormal and tangent directions, as well as anholonomic coordinates, to recognize motions across surfaces, as well as their connection with solitonic equations. In addition, this study examines at normal motion for spacelike curve functions, using anholonomic coordinates to control motion in normal and binormal directions and analyzing the resulting soliton equations. This work emphasizes the detailed connection between surface motion and anholonomic coordinates, which is fundamental for understanding the many behaviors presented by spacelike curves in Minkowski space and their importance in soliton equations. This paper demonstrates the complex connection between surface motion and anholonomic coordinates, which is important for understanding the many behaviors displayed by spacelike curves in Minkowski space and their significance in soliton equations.