Totally real submanifolds in a 6-sphere (Q1191398)
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scientific article; zbMATH DE number 59879
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Totally real submanifolds in a 6-sphere |
scientific article; zbMATH DE number 59879 |
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Totally real submanifolds in a 6-sphere (English)
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27 September 1992
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Consider the 6-dimensional Riemannian sphere \(S^ 6\) with constant curvature 1 endowed with the nearly Kähler structure induced from the Cayley divison algebra. Suppose that \(M\) is a 3-dimensional compact totally real submanifold of \(S^ 6\) and let \(k_ 0\) be the infimum of the sectional curvature of \(M\). The author proves that either \(4k_ 0\leq 1\) or \(M\) is totally geodesic.
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curvature bound
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nearly Kähler structure
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Cayley divison algebra
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