Biharmonic S-curves according to Sabban frame in Heisenberg group Heis³

Abstract

In this paper, we study biharmonic curves accordig to Sabban frame in the Heisenberg group Heis³. We characterize the biharmonic curves in terms of their geodesic curvature and we prove that all of  biharmonic curves are helices in the Heisenberg group Heis³. Finally, we find out their explicit parametric equations according to Sabban Frame.