A New Method for Designing Involute Trajectory Timelike Ruled Surfaces in Minkowski 3-space

Bilici M.

Boletim da Sociedade Paranaense de Matematica, cilt.41, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41
  • Basım Tarihi: 2023
  • Doi Numarası: 10.5269/bspm.51594
  • Dergi Adı: Boletim da Sociedade Paranaense de Matematica
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: developable surface, Frenet frame, involute-evolute, Minkowski 3-space, Trajectory ruled surface
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this study, we present the new concept of involute trajectory ruled surface in Minkowski 3-space. The involute trajectory timelike ruled surface is a surface generated by the motion of a timelike oriented line X along the spacelike involute curve γ (s) of a given timelike base curve r (s). The main purpose of this article is to present a new perspective on the generation of developable trajectory ruled surfaces in Minkowski 3-space. These surfaces are formed depending on the angle θ between the Darboux vector D and the binormal vector b of the evolute curve r (s). Also, some new results and theorems related to the developability of the involute trajectory timelike ruled surfaces are obtained. Finally, we illustrate these surfaces by presenting one example.