Adjoint transform of Willmore surfaces in |
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Authors: | Xiang Ma |
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Institution: | (1) School of Mathematical Sciences, Peking University, 100871 Beijing, P. R. China |
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Abstract: | Using moving frame method, we study the Möbius geometry of a pair of conformally immersed surfaces in
. 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
. 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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Keywords: | 53A30 53A55 53C42 53C43 |
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