Schrödinger flow of maps into symplectic manifolds

Abstract

The definition of Schrodinger flow is proposed. It is indicated that the flow of ferromagnetic chain is actually Schrodinger flow of maps intoS 2, and that there exists a unique local smooth solution for the initial value problem of one-dimensional Schrodinger flow of maps into Kahler manifolds. In case the targets are Kahler manifolds with constant curvature, it is proved that one-dimensional Schrodinger flow admits a unique global smooth solution.