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Dede M., Çimdiker Aslan M., Ekici C.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.44, no.17, pp.12630-12639, 2021 (SCI-Expanded)
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MATHEMATICAL METHODS IN THE APPLIED SCIENCES
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
B-Darboux frame, curve framing, generalized relaxed elastic line, intrinsic equations, variational problem, RELAXED ELASTIC LINE, INTRINSIC EQUATIONS, CURVES
Eskisehir Osmangazi University Affiliated:
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.