On some new frames along a space curve and integral curves with Darboux q-vector fields in E3

UYAR DÜLDÜL B.

AIMS Mathematics, cilt.9, sa.7, ss.17871-17885, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 7
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3934/math.2024869
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.17871-17885
  • Anahtar Kelimeler: integral curve, normal q-frame, osculating q-frame, q-frame, rectifying q-frame
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, to start we defined osculating q-frame, normal q-frame, and rectifying q frame along a space curve in Euclidean 3-space E3 by using the Darboux vector field of the q-frame. We obtained the derivative equations of these new frames. Later, we defined some new integral curves of a space curve and called them do-direction curve, dn-direction curve and dr-direction curve. Finally, we gave some theorems and results related with these curves.