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Willmore Surfaces of ℝ4 and the Whitney Sphere

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We make a contribution to the study of Willmore surfaces infour-dimensional Euclidean space ℝ4 by making useof the identification of ℝ4 with two-dimensionalcomplex Euclidean space ℂ2. We prove that theWhitney sphere is the only Willmore Lagrangian surface of genus zero inℝ4 and establish some existence and uniquenessresults about Willmore Lagrangian tori in ℝ4≡ ℂ2.

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Castro, I., Urbano, F. Willmore Surfaces of ℝ4 and the Whitney Sphere. Annals of Global Analysis and Geometry 19, 153–175 (2001). https://doi.org/10.1023/A:1010720100464

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