f-Biharmonic Curves in the Three-dimensional Para-Sasakian Space Forms

In this paper, we give some characterizations for proper f-biharmonic curves in the para-Bianchi-Cartan-Vranceanu space forms with 3-dimensional para-Sasakian structures.

On characterization of horizontal biharmonic curves in H^2 × R

In this paper, we study biharmonic curves in H2 × R. We show that all of them are helices. By using the curvature and torsion of the curves, we give some characterizations of horizontal biharmonic curves in H2 × R.

Classification of f-Biharmonic Curves in Lorentz–Minkowski Space

In this paper, we firstly derived the equations for the curves of a Lorentz–Minkowski space L3 to be f-biharmonic. Then, using these equations, we classify such unit speed curves in L3.

f−BIHARMONIC CURVES WITH TIMELIKE NORMAL VECTOR ON LORENTZIAN SPHERE

In this paper, we study $f-$biharmonic curves as the critical points of the $f-$bienergy functional $E_{2}(\psi )=\int_{M}f\mid \tau (\psi )^{2}\mid \vartheta _{g}$, on a Lorentzian para-Sasakian manifold $M$. We give necessary and sufficient conditions for a curve such that has a timelike principal normal vector on lying 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 $S_{1}^{4}.$