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 Biharmonic curves in 3-dimensional Lorentzian Sasakian space forms Commun. Korean Math. Soc.Published online May 21, 2020 Ji-Eun Lee Chonnam National University Abstract : In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms $\mathcal{M}_1^3 (H)$ except the case constant curvature $-1$. Next, we find that for a slant curve in a $3$-dimensional Sasakian Lornetzian manifold, its ratio of geodesic curvature" and geodesic torsion $-1$" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with $\kappa^2-\tau^2=-1+\varepsilon_1(H+1)\eta(B)^2$ in the Lorentzian Sasakian space forms $\mathcal{M}_1^3 (H)$ except the case constant curvature $-1$. As example, we classify proper biharmonic Frenet curves in $3$-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix. Keywords : Slant curves, Legendre curves, biharmonic, Lorentzian Sasakian space forms MSC numbers : 53C25, 53C50 Full-Text :