Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3
In this paper, we study spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3 . We show that spacelike biharmonic curves are general helices. We characterize position vector of spacelike biharmonic general helices in terms of their curvature and torsion.
The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces
In this article we characterize all biharmonic curves of the Cartan-Vranceanu 3-dimensional spaces and we give their explicit parametrizations.
Biharmonic curves in 3-dimensional Sasakian space forms
AbstractWe show that every proper biharmonic curve in a 3-dimensional Sasakian space form of constant holomorphic sectional curvature H is a helix (both of whose geodesic curvature and geodesic torsion are constants). In particular, if H ≠  1, then it is a slant helix, that is, a helix which makes constant angle α with the Reeb vector field with the property
$$\kappa^{2}+\tau^{2}=1+(H-1)\sin^{2}\alpha$$. Moreover, we construct parametric equations of proper biharmonic herices in Bianchi–Cartan–Vranceanu model spaces of a Sasakian space form.