Towards an algebro-geometric interpretation of the neumann system

Lax equations and constants of motion for C. Neumann's system of constrained harmonic oscillators are derived in a systematic wayfrom the Burchnall-Chaundy-Krichever theory of 2nd-order differential operators D²+q(t). The approach is based on a geometric step: to map the algebraic curve and linebundle associated with D² + q(t) to a larger projective space by means of a suitable linear system. The image of D2 + q(t) is, roughly speaking, just the Lax operator for the Neumann system.