Surfaces in Euclidean space with conformal Gauss map (Q2781737)
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scientific article; zbMATH DE number 1721697
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Surfaces in Euclidean space with conformal Gauss map |
scientific article; zbMATH DE number 1721697 |
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17 October 2002
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surface
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conformal Gauss map
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Veronese surface
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Surfaces in Euclidean space with conformal Gauss map (English)
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In this paper, the author proves: Let \(M\) be an orientable surface of the \(n\)-dimensional Euclidean space, then its Gauss map \(g: M \to G_{2,n}\) is conformal and totally real if and only if \(M\) is a pseudo-umbilical, flat surface. Combining this, with \textit{M. Obata}'s result [J. Differ. Geom. 2, 217-223 (1968; Zbl 0181.49801)], \textit{S.-T. Yau}'s result [Am. J. Math. 96, 346-366 (1985; Zbl 0304.53041)] and \textit{R.-L. Bryant}'s result [Trans. Am. Math. Soc. 290, 259-271 (1985; Zbl 0572.53002)], he gives a new characterization of Veronese surface.
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