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

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.