Rectifying curves in the three-dimensional sphere

Rectifying curves in R3 were introduced by B.Y. Chen in 2003 as space curves whose position vector always lies in its rectifying plane. In this paper, we extend this definition, as well as several results about rectifying curves obtained by Chen and Dillen (2005) and Izumiya and Takeuchi (2004), to curves in the three-dimensional sphere. Our results give nice and relevant differences between spherical and Euclidean geometries.