Bertrand Offsets of Ruled Surfaces with Darboux Frame

Şentürk G. Y., YÜCE S.

Results in Mathematics, vol.72, no.3, pp.1151-1159, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1007/s00025-016-0571-6
  • Journal Name: Results in Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1151-1159
  • Keywords: Ruled surface, Bertrand, Darboux frame
  • Istanbul Gelisim University Affiliated: No


In this study, using Darboux frame T, g, n of ruled surface φ(s, v) , Bertrand offset φ∗(s, v) of ruled surface φ(s, v) is identified. Characteristic properties of Bertrand mates of ruled surfaces as a striction curve, distribution parameter and orthogonal trajectories are examined according to Darboux frame. We have examined the relations between the distribution parameters of the ruled surfaces which are generated by the Darboux frames vectors of the ruled surfaces φ and φ∗.