Exploring Hasimoto surfaces within equiform geometry in Minkowski space

Abstract In this study, we investigate the equiform geometry of Hasimoto surfaces within the context of three-dimensional Minkowski space. We analyze the geometric characteristics inherent to these surfaces, focusing on their Gaussian and mean equiform curvatures. This analysis encompasses three distinct scenarios involving non-lightlike curves. Additionally, we propose a method for characterizing the parameter curves associated with the equiform Hasimoto surfaces in Minkowski space. To illustrate our findings, we present several examples of these surfaces within this geometric framework.