On Characterization of Time-Like Horizontal Biharmonic Curves in the Lorentzian Heisenberg Group Heis³

Abstract

In this paper, we study energy of time-like horizontal biharmonic curves in the Lorentzian Heisenberg group Heis 3 . We characterize the biharmonic curves in terms of their curvature and torsion. We prove that all of the biharmonic curves are helices. Finally, we study the mechanics of biharmonic curves and provide conditions for energy of horizontal biharmonic curves