Helices with $ F $-constant vector fields in the Euclidean space $ \mathbb{E}^4 $
Abstract
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Mathematics and Applications
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 2
- Pages
- 4299–4334
- Publication date
- 1 January 2026