Minimal Curves on Ruled Surfaces Generated by Legendre Curves

Year 2024, Issue: 49, 43 - 52, 31.12.2024

Yusuf Yaylı , İsmet Gölgeleyen

https://doi.org/10.53570/jnt.1545097

Abstract

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.

Keywords

Legendre curves, minimal curves, B-scroll surfaces

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