On a variational problem due to the B-Darboux frame in Euclidean 3-space
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.44, sa.17, ss.12630-12639, 2021 (SCI-Expanded, Scopus)
- 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.