Null biharmonic curves in the Lorentzian Heinsenberg group Heis3

Abstract

In this paper, we study biharmonic curves and we characterize null biharmonic curves in terms of their curvature and torsion in the Lorentzian Heisenberg group Heis3. We give necessary and sufficient conditions for null biharmonic curves in the Lorentzian Heisenberg group Heis3. Finally, we prove that all of null biharmonic curves are helices and we give their explicit parametrizations.