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Adjoint Transform of Willmore Surfaces in $n$-sphere

Xiang Ma
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Abstract

After the surface theory of Möbius geometry, this study concerns a pair of conformally immersed surfaces in $n$-sphere. Two new invariants $θ$ and $ρ$ associated with them are introduced as well as the notion of touch and co-touch. This approach is helpful in research about transforms of certain surface classes. As an application, we define adjoint transform for any given Willmore surface in $n$-sphere. It always exists locally (yet not unique in general) and generalizes known duality theorems of Willmore surfaces. This theory on surface pairs reaches its high point by a characterization of adjoint Willmore surfaces in terms of harmonic maps.

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Xiang Ma. 2005-08-08. Adjoint Transform of Willmore Surfaces in $n$-sphere. https://doi.org/10.1007/s00229-006-0635-0

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