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- W2963150448 abstract "The classification of Willmore two-spheres in the $n$-dimensional sphere $S^n$ is a long-standing problem, solved only when $n = 3, 4$ by Bryant, Ejiri, Musso and Montiel independently. In this paper we give a classification when $n = 5$. There are three types of such surfaces up to Mobius transformations: (1) superconformal surfaces in $S^4$; (2) minimal surfaces in $R^5$; (3) adjoint transforms of superconformal minimal surfaces in $R^5$. In particular, Willmore surfaces in the third class are not $S$-Willmore (i.e., without a dual Willmore surface). To show the existence of Willmore two-spheres in $S^5$ of type (3), we describe all adjoint transforms of a superconformal minimal surface in $R^n$ and provide some explicit criterions on the immersion property. As an application, we obtain new immersed Willmore two-spheres in $S^5$ and $S^6$, which are not $S$-Willmore." @default.
- W2963150448 created "2019-07-30" @default.
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- W2963150448 date "2017-06-01" @default.
- W2963150448 modified "2023-10-16" @default.
- W2963150448 title "Classification of Willmore two-spheres in the 5-dimensional sphere" @default.
- W2963150448 doi "https://doi.org/10.4310/jdg/1497405626" @default.
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