A generalization of the notion of helix

Authors: PASCUAL LUCAS, JOSE ANTONIO ORTEGA-YAGUES

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.

Keywords: Helix, osculating helix, normal helix, rectifying helix, Darboux vector, $F$-constant vector field

Full Text: PDF