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 Heisen berg group Heis(3) We characterize the biharmonic curves in terms of then 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