On characterization of spacelike dual biharmonic curves in dual Lorentzian Heisenberg group DHeis33

Abstract

In this paper, we study spacelike dual biharmonic curves. We characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the Lorentzian dual Heisenberg group D-Heis3(3). We give necessary and sufficient conditions for spacelike dual biharmonic curves in the Lorentzian dual Heisenberg group D-Heis3(3). Therefore, we prove that all spacelike dual biharmonic curves are spacelike dual helix. Moreover, we give their explicit parametrizations of spacelike dual biharmonic curves. Finally, we illustrate our main results in Figs. 1 and 2.