A Legendrian mKdV relative equilibrium on an embedded torus

A closed Legendrian curve in the Heisenberg group moved by the Hamiltonian flow of horizontal length (rotation angle 12π/7 per curvature period, p/q = 6/7), drawn in unscaled group coordinates. Drag to rotate; scroll or pinch to zoom.

Speed

Reeb gauge

Periodic gauge (Reeb term c₀ξ): the curve stays on the torus

Normalization C(t) = 0: the curve drifts by −c₀t

Show

Torus

See-through torus

Points on the curve

One point 14 points

Trace of the first point

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