The Ruled Surface Obtained by the Natural Mate Curve

Güler F.

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, vol.41, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41
  • Publication Date: 2023
  • Doi Number: 10.5269/bspm.51670
  • Journal Name: BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Keywords: Curves, ruled surfaces, developable surfaces, minimal surfaces
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

The natural mate curve r1 of r is defined the integral of principal normal vector with any parameter s, of a curve r. We investigate the ruled surface generated by the natural mate curve of any Frenet curve r = r(s) in the Euclidean 3-space. We obtained some necessary and sufficient conditions for this surface to be developable and minimal ruled surface. We research related to be the asymptotic curve and the geodesic curve of the base curve on the ruled surface. Example of our main results are also presented.