Rectifying Curves in the Three-Dimensional Hyperbolic Space

Abstract

B. Y. Chen introduced rectifying curves in \({\mathbb{R}^3}\) as space curves whose position vector always lies in its rectifying plane. Recently, the authors have extended this definition (as well as several results about rectifying curves) to curves in the three-dimensional sphere. In this paper, we study rectifying curves in the three-dimensional hyperbolic space, and obtain some results of characterization and classification for such kind of curves. Our results give interesting and significant differences between hyperbolic, spherical and Euclidean geometries.