In this paper, we first give a characterization of an f-biharmonic curve γ :(a, b) → Nn(C) in an n-dimensional space form by solving ODEs. We also give complete classifications of proper f-biharmonic curves in a 3-dimensional sphere S3 and a hyperbolic space H3 . We also derive f-biharmonic Riemannian submersion equation from 3-manifolds. We then use it to study f-biharmonic Riemannian submersions from a 3-space form M3 (c) to a 2-space form N2 (c) with constant sectional curvature c, and also construct many proper f-biharmonic Riemannian submersions from ℝ3, H3 , Sol space and a product space S2\{N, S} × ℝ.
2020 Mathematics Subject Classification. 58E20, 53C12.