Special periodic solutions of Schrödinger flow (Q851012)

The authors study the Schrödinger flow -- a Hamiltonian flow on the space of mappings from a closed Riemannian manifold \((M,g)\) to a closed Kähler manifold \((N,h,J)\) - where \(J\) is the complex structure of \(N\) and \(h\) is a Kähler metric. An existence theorem is proved for the case when \(N=S^2\) and \(M\) admits an isometry \(T:M\to M\) such that \(T^2=I\). Then, it is shown that the Schrödinger flow on mappings from \(S^2\) into \(S^2\) admits for any \(\lambda>0\) an infinite number of inequivalent periodic solutions with period \(2\pi/\lambda\).