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

Abstract

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.

Keywords

• sl2ℝ˜\widetilde {{\rm{s}}{{\rm{l}}_2}\mathbb{r}} space
• iii-harmonic curves
• biharmonic curves
• general helix
• 53c30
• 53a40
• 53b25
• 58e20