Helices with $ F $-constant vector fields in the Euclidean space $ mathbb{E}^4 $


Sağlam D., Selvi U., Babadağ F., Atasoy A.

AIMS MATHEMATICS, cilt.11, sa.2, ss.4299-4334, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3934/math.2026173
  • Dergi Adı: AIMS MATHEMATICS
  • Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), Directory of Open Access Journals
  • Sayfa Sayıları: ss.4299-4334
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet

Özet

This study aims to investigate the geometric properties of $V_i$-helices in the four-dimensional Euclidean space $\mathbb{E}^4$, considering Frenet vector fields as instances of $F$-constant vector fields. For each $i \in \{1, 2, 3, 4\},$ the necessary and sufficient conditions for $V_i$-helices are derived in terms of their curvatures, and a generalization of these helices is presented. Examples of these structures are provided, and their projections onto three-dimensional (3D) spaces are visualized using Python. Furthermore, the corresponding Python codes are included in the Appendix.