Time-like curves in Minkowski space exploring anholonomic coordinates surface interactions and soliton connections

By studying the differential geometry of time-like curves in Minkowski space, the paper emphasizes how important anholonomic coordinates are to comprehending the geometric and physical characteristics of these curves. The study investigates the osculating motion of time-like curves, where independent surfaces are defined using anholonomic coordinates in the tangent and normal directions. In order to develop unique surface structures, it goes further into the rectifying motion of these curves by combining tangent and binormal directions. Additionally, the study reveals complex connections between anholonomic coordinates and the various time-like curve behaviors, giving a systematic structure for analyzing them. Lastly, Lamb’s formulation highlights the relationship between space curves and solitons, implications for both geometry and physics.