Constructing a completely integrable system via algebrogeometric data

Abstract

We use the algebro-geometric data given by a genus-2 Jacobian, a curve and aline bundle on the Jacobian, and the action of a group of translates on the thetasections of this line bundle, to reconstruct an integrable system: the geodesicmotion onSO(4), metric II (so termed after Adler and van Moerbeke).