On a variational problem due to the B-Darboux frame in Euclidean 3-space

Dede M., Çimdiker Aslan M., Ekici C.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.44, sa.17, ss.12630-12639, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 17
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1002/mma.7567
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.12630-12639
  • Anahtar Kelimeler: B-Darboux frame, curve framing, generalized relaxed elastic line, intrinsic equations, variational problem, RELAXED ELASTIC LINE, INTRINSIC EQUATIONS, CURVES
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a new frame which is called the B-Darboux frame on a surface in Euclidean 3-space. We know that the parallel transport frame is derived from the Frenet frame along a space curve on a surface. Analogously, we derive the B-Darboux frame from the Darboux frame along a space curve on a surface in Euclidean 3-space. Then, we obtain the intrinsic equations due to the B-Darboux frame for a generalized relaxed elastic line on an oriented surface and give some applications of this obtained results in Euclidean 3-space.