In this paper, we study f−biharmonic curves as the critical points of the f−bienergy functional. We give necessary and sufficient conditions for a curve having a timelike binormal vector lying on a 4-dimensional conformally flat, quasi-conformally flat and conformally symmetric Lorentzian para-Sasakian manifold to be an f−biharmonic curve. Moreover, we introduce proper f−biharmonic curves on the Lorentzian sphere .
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