Abstract
Using moving frame method, we study the Mobius geometry of a pair of conformally immersed surfaces in Open image in new window. Two new invariants θ and ρ associated with them arise naturally as well as the notion of touch and co-touch. As an application, adjoint transform is defined for any Willmore surface in Open image in new window. It always exists locally, hence generalizes known duality theorems of Willmore surfaces. Finally we characterize a pair of adjoint Willmore surfaces in terms of harmonic map.
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