The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics
Velimir Jurdjevic · arXiv (Cornell University) · 2007
This paper defines a symplectic form on the infinite dimensional Fréchet manifold of framed curves of fixed length over a simply connected Riemannian manifold of constant curvature. The paper then considers Hamiltonian systems generated by the geometric invariants of the curves on the base manifold and relates them to the equations of mathematical physics.