Schrödinger Maps and their associated Frame Systems

Abstract

In this paper we establish the equivalence of solutions between Schrödinger map into ${\mathbb{S}}^2$ or ${\mathbb{H}}^2$ and their associated gauge invariant Schrödinger equations. We also establish the existence of global weak solutions into ${\mathbb{H}}^2$ in two space dimensions. We extend these ideas for maps into compact hermitian symmetric manifolds with trivial first cohomology.

19 pages, submitted