Triviality of the dressing isotropy for a Smyth-type potential and nonclosing of the resulting CMC surfaces

Details Triviality of the dressing isotropy for a Smyth-type potential and nonclosing of the resulting CMC surfaces Triviality of the dressing isotropy for a Smyth-type potential and nonclosing of the resulting CMC surfaces

2010-09-23

arxiv.org/abs/1009.4584v1

"Differential Geometry and its Applications", Iasi, proceedings, 2011, 61-70

Mathematics

Differential Geometry

8 pages

Scientific paper

The quantum cohomology of CP^1 is generated by some potential (Frobenius manifold) that also has an interpretation as a potential of some harmonic map. Actually, the potential induces harmonic maps into three different symmetric spaces and each of these harmonic maps induces an immersion of an integrable surface. The final goal of this paper is to investigate if any of the associated immersions closes around the singularity at z=0 (none does). The crucial tool for deciding this question is the main technical result of the paper, which states that the dressing isotropy of the CP^1 potential is trivial.

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