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This paper defines a symplectic form on the infinite dimensional Fr\'echetmanifold of framed curves of fixed length over a simply connected Riemannianmanifold of constant curvature. The paper then considers Hamiltonian systemsgenerated by the geometric invariants of the curves on the base manifold andrelates them to the equations of mathematical physics.

The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics