On the dual pseudo-spherical elastic curves

ÖZKAN TÜKEL G., YÜCESAN A.

Turkish Journal of Mathematics, cilt.48, sa.3, ss.623-633, 2024 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.55730/1300-0098.3529
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.623-633
  • Anahtar Kelimeler: Calculus of variations, dual pseudo-sphere, dual pseudo-spherical elastic curve, elastic strips
  • Isparta Uygulamalı Bilimler Üniversitesi Adresli: Evet

Özet

We investigate a dual bending energy functional that operates on the dual pseudo-sphere in dual Lorentzian space. For a nonnull dual curve on the dual pseudo-sphere to be considered elastic, it must satisfy the conditions of a dual Euler-Lagrange equation. To solve this problem, we use Jacobi elliptic functions to approach the real part and the integral factors method to solve the dual part. Using E. Study mapping, we examine situations where every timelike or spacelike dual elastic curve on the dual pseudo-sphere matches an elastic strip with a suitable base curve in Minkowski 3-space.