Elastic curves and Willmore Hopf-Tori

Finite type curves in S 2ReconstructionVia the double cover SU 2 → SO 3 the extended frame equation canbe written as( )F λ ′ = F iλ κλwhere λ ∈ R .−κ −iλThe associate family of curves R → SU 2 ∩ R 3 ∼ = S 2 given byγ λ = F λ F −1−λhas geodesic curvature λ −1 κ, and constant speed |λ|.Call the evaluation points the sym points (w.l.o.g. take λ = 1).