Elastic curves and Willmore Hopf-Tori
Elastic curves and Willmore Hopf-Tori
Elastic curves and Willmore Hopf-Tori
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Moduli space of constrained elasticaLemmaThe conformal type of a constrained <strong>Willmore</strong> <strong>Hopf</strong>-torus isτ = A 4π + iL { ω4π = 2 + iL4πfor wave-like ,ω−lfor orbit-like2+ iL4πProof.Computing A using Gauss-Bonnet givesA = 2πω − l∫ ρwhere ρ is the period of κ. A computation gives∫ ρ{ 0 for wave-like ,κ =2π for orbit-like00κ
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