There exist no 2-type surfaces in \(E^ 3\) which are images under stereographic projection of minimal surfaces in \(S^ 3\) (Q1202525)
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scientific article; zbMATH DE number 109067
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | There exist no 2-type surfaces in \(E^ 3\) which are images under stereographic projection of minimal surfaces in \(S^ 3\) |
scientific article; zbMATH DE number 109067 |
Statements
There exist no 2-type surfaces in \(E^ 3\) which are images under stereographic projection of minimal surfaces in \(S^ 3\) (English)
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25 February 1993
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B.-Y. Chen stated the following conjecture in 1985: The only compact finite type surface in \(E^ 3\) is the sphere. The conjecture is still standing. The present paper deals with a particular case of the conjecture. The following theorems are proved. Theorem 1. There exist no 2-type surfaces in \(E^ 3\) that are the image of minimal surfaces in \(S^ 3\) under stereographic projection. Theorem 2. There exist no complete 2-type Willmore surfaces in \(E^ 3\) with non-negative Gaussian curvature.
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2-type surfaces
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minimal surfaces
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Willmore surfaces
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