@article{Sağlam2026, 
author = {Derya Sağlam and Umut Selvi and Faik Babadağ and Ali Atasoy},
title = {Helices with    F-constant vector fields in the Euclidean space              E        4},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4299-4334},
keywords = {Vi-helix, Darboux vector field, F-constant vector field, Frenet-Serret vector field, cylinder},
url = {https://www.sciopen.com/article/10.3934/math.2026173},
doi = {10.3934/math.2026173},
abstract = {This study aims to investigate the geometric properties of        V    i  -helices in the four-dimensional Euclidean space              E        4  , considering Frenet vector fields as instances of    F-constant vector fields. For each    i  ∈  {  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.}
}