Elastic curves and Willmore Hopf-Tori

Moduli space of constrained elasticaConstrained elastica all arise from a simple ’translational’ Whithamflow of elastica.TheoremThe moduli space of closed constrained elastica is the cartesianproduct of the 1-dimensional moduli space of closed elastica withthe half-open interval [0, 1).CorollaryThe moduli space of closed constrained elastica has two connectedcomponents, one for each homotopy type.