Construction of surface pencil with a given spacelike adjoint curve

Guler F.

Advanced Studies: Euro-Tbilisi Mathematical Journal, cilt.15, sa.2, ss.1-11, 2022 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.32513/asetmj/19322008213
  • Dergi Adı: Advanced Studies: Euro-Tbilisi Mathematical Journal
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.1-11
  • Anahtar Kelimeler: asymptotic curve, geodesic curve, line of curvature, Minkowski space, surface pencil
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

The adjoint curve of any Frenet curve r=r(s) is defined as the integral of binormal vector with any parameter s, of a curve r. In this paper,we analyzed the problem of finding a surfaces pencil through a given the spacelike adjoint curve as an asymptotic curve, geodesic or a line of curvature in Minkowski 3-space, respectively. We find necessary and sufficient condition for a surface pencil possessing the spacelike adjoint curve as an asymptotic curve, geodesic or line of curvature. We illustrate this method by presenting some examples.