Curves whose pseudo spherical indicatrices are elastic

YÜCESAN A., ÖZKAN TÜKEL G., TURHAN T.

Turkish Journal of Mathematics, cilt.42, sa.6, ss.3123-3132, 2018 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 6
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1801-44
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.3123-3132
  • Anahtar Kelimeler: Elastic curve, Euler-Lagrange equation, Pseudo spherical indicatrix
  • Isparta Uygulamalı Bilimler Üniversitesi Adresli: Evet

Özet

The pseudo spherical indicatrix of a curve in Minkowski 3-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve. The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter 2-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve. In this paper, we separately derive Euler-Lagrange equations of all pseudo spherical indicatrix elastic curves in terms of the causal character of a curve in Minkowski 3-space. Then we give some results of solutions of these equations.