Exploring helices in Minkowski $3$-space $\mathbb{E}_{1}^{3}$
Esra Betül Koç Öztürk, Ufuk Öztürk · Tamkang Journal of Mathematics · 2024
This study focuses on the geometric exploration of helices in Minkowski $3-$ space. For this purpose, we study the problem of constructing a spacelike general helix, slant helix, or Darboux helix with a timelike principal from a given plane curve, fixed vector, and constant angle. We obtain a parametric representation for the helices whose projection is onto the plane $P$ perpendicular to the fixed vector $U$ share the same fixed vector. In addition, we furnish various illustrative examples showcasing the geometric characteristics of these helices.