Biharmonic curves in Lorentz Heisenberg Group H_3

Abstract

The aim of this paper is the characterization of biharmonic curves in the $3-$ dimensional Lorentz-Heisenberg group $\mathcal{H}_{3}$ endowed with a left invariant Lorentzian metric $g_{i}$ in the two following cases: \begin{enumerate} \item $g_{1}=-dx^{2}+dy^{2}+(xdy+dz)^{2},$ \item $g_{2}=dx^{2}+dy^{2}-(xdy+dz)^{2}.$ \end{enumerate}