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