Rigidity of the Clifford tori in \(S^3\) (Q1095418)
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scientific article; zbMATH DE number 4028349
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rigidity of the Clifford tori in \(S^3\) |
scientific article; zbMATH DE number 4028349 |
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Rigidity of the Clifford tori in \(S^3\) (English)
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1988
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Let M be a Clifford torus in the 3-dimensional unit sphere \(S^ 3\) and let \(i: M\to S^ 3\) be the inclusion map. Suppose that \(\{f_ t\}\) is a smooth one-parameter family of isometric immersions of M into \(S^ 3\) with \(f_ 0=i\). In this paper, we prove that for each t, there exists an isometry \(\psi _ t\) of \(S^ 3\) such that \(f_ t=\psi _ t\circ i\).
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Clifford torus
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isometric immersions
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rigidity
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