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, vol.44, no.17, pp.12630-12639, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 17
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.7567
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: 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
  • Page Numbers: pp.12630-12639
  • Keywords: B-Darboux frame, curve framing, generalized relaxed elastic line, intrinsic equations, variational problem, RELAXED ELASTIC LINE, INTRINSIC EQUATIONS, CURVES
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

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.