In any 2-dimensional space form, discrete elastic curves are the 2-invariant curves and discrete area-constrained elastic curves are the 3-invariant curves of Bäcklund transformation flows.
Constant mean curvature tori in terms of elliptic functions.Journal für die reine und angewandte Mathematik, 374:169–192, 1987
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Discrete curve theory in space forms: planar elastic and area-constrained elastic curves
In any 2-dimensional space form, discrete elastic curves are the 2-invariant curves and discrete area-constrained elastic curves are the 3-invariant curves of Bäcklund transformation flows.