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

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

2007-08-09

arxiv.org/abs/0708.1202v1

Mathematics

Symplectic Geometry

Scientific paper

This paper defines a symplectic form on the infinite dimensional Fr\'echet
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.

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