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Isothermic surfaces in $$S^n$$ S n are characterised by the existence of a pencil $$\nabla ^t$$ ∇ t of flat connections. Such a surface is special of type $$d$$ d if there is a family $$p(t)$$ p ( t ) of $$\nabla ^t$$ ∇ t -parallel sections whose dependence on the spectral parameter $$t$$ t is polynomial of degree $$d$$ d . We prove...
We define a transformation on harmonic maps $${N:\,M \to S^2}$$ from a Riemann surface M into the 2-sphere which depends on a parameter $${\mu \in \mathbb{C}_*}$$ , the so-called μ-Darboux transformation. In the case when the harmonic map N is the Gauss map of a constant mean curvature surface $${f:\,M \to \mathbb{R}^3}$$ and μ is real, the Darboux transformation of −N is the Gauss map...
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