Minimal Curves on Ruled Surfaces Generated by Legendre Curves

In this paper, we study the conditions under which Legendre curves on ruled surfaces are classified as minimal loci. By investigating the scenario where the directive curve is a binormal vector, we establish the criteria for these curves to have minimal loci on B-scroll-ruled surfaces. Furthermore, we present illustrative examples showcasing concrete instances of minimal curves within this context. Finally, we discuss the need for further research.