f-Biharmonic curves in space forms and f-biharmonic Riemannian submersions from 3-manifolds

In this paper, we first give a characterization of an f -biharmonic curve γ :(a, b) → N n (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 S 3 and a hyperbolic space H 3 . 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 M 3 (c) to a 2-space form N 2 ( c ) with constant sectional curvature c , and also construct many proper f -biharmonic Riemannian submersions from ℝ 3 , H 3 , Sol space and a product space S 2 \{ N, S } × ℝ. 2020 Mathematics Subject Classification. 58E20, 53C12.