Elastic curves and Willmore Hopf-Tori
Elastic curves and Willmore Hopf-Tori
Elastic curves and Willmore Hopf-Tori
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Polynomial Killing fields <strong>and</strong> spectral curvePolynomial Killing fieldsFinite type <strong>curves</strong>A finite type curve R → S 2 is one whose extended frame satisfiesF ′ λ = 1 2 F λ V (X) , F λ (0) = 1for some polynomial Killing field X.Let X(0) = X 0 . ThenF −1λ X 0F λ = X ,so det X = det X 0 is independent of arc-length. By thetwistedness condition det X is an even polynomial.