Turkish Journal of Mathematics
Abstract
In this paper we generalize the notion of helix in the three-dimensional Euclidean space, which we define as that curve $\alpha$ for which there is an $F$-constant vector field $W$ along $\alpha$ that forms a constant angle with a fixed direction $V$ (called an axis of the helix). We find the natural equation and the geometric integration of helices $\alpha$ where the $F$-constant vector field $W$ is orthogonal to its axis.
DOI
10.55730/1300-0098.3418
Keywords
Helix, osculating helix, normal helix, rectifying helix, Darboux vector, $F$-constant vector field
First Page
1158
Last Page
1168
Recommended Citation
LUCAS, P, & ORTEGA-YAGUES, J. A (2023). A generalization of the notion of helix. Turkish Journal of Mathematics 47 (4): 1158-1168. https://doi.org/10.55730/1300-0098.3418
