III-harmonic Curves in SL2ℝ˜ \widetilde {{\rm{S}}{{\rm{L}}_2}\mathbb{R}} Space

Some work has been done in the study of non-geodesic III-harmonic curves in some model spaces. In this paper, we study III-harmonic curves in SL2ℝ˜ \widetilde {{\rm{S}}{{\rm{L}}_2}\mathbb{R}} space. We give necessary and su cient conditions for helices to be III-harmonic. Also, we characterize III-harmonic curves in terms of their curvature and torsion.