Framed Curves and Their Applications Based on a New Differential Equation

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Yazıcı B., Karakus¸ S., Tosun M.

International Electronic Journal of Geometry, cilt.15, ss.41-56, 2022 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15
  • Basım Tarihi: 2022
  • Doi Numarası: 10.36890/iejg.875477
  • Dergi Adı: International Electronic Journal of Geometry
  • Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.41-56
  • Anahtar Kelimeler: Framed curves, framed helices, framed rectifying curves, framed spherical curves, singular points
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

Characterization is very important for non-regular curves in differential geometry. Recently, the concept of framed curve has been proposed to examine a non-regular curve. Framed curves are defined as smooth curves with a moving frame that can have singular points. In this paper, the differential equation is obtained by using distance squared functions for framed curves with for each p, q= 0 framed curvatures in Euclidean space. Next, we give the relationships between the differential equation and some special curves. Moreover we introduce a new equation of framed helices with the help of the differential equation. Moreover, these are supported by some examples and figures.