Grassmann geometry of 6-dimensional sphere. II (Q2765979)
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scientific article; zbMATH DE number 1695252
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Grassmann geometry of 6-dimensional sphere. II |
scientific article; zbMATH DE number 1695252 |
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16 March 2003
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submanifolds of \(\mathbb{S}^6\)
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Riemannian manifold
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Grassmann bundle
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0.90474635
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0.86989355
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0.8693498
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0.8615035
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0.86113316
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Grassmann geometry of 6-dimensional sphere. II (English)
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For a Riemannian manifold \((M,g)\) denote by \(G_p(T_xM)\) the Grassmann manifold of all oriented \(p\)-dimensional linear subspaces of the tangent space \(T_xM\) of \(M\) at \(x\in M\) and by \(G_p(TM)\) the Grassmann bundle \(\cup_{x\in M}G_p(T_xM)\). Let \(\Sigma\) be a subbundle of \(G_p(TM)\). A \(p\)-dimensional submanifold \(N\) of \(M\) is called a \(\Sigma\)-submanifold if \(T_xN \in\Sigma\) holds for any \(x\in N\). In this paper the authors study the existence and nonexistence of \(\Sigma\)-submanifolds of \(\mathbb{S}^6\).NEWLINENEWLINENEWLINEPart I, cf. Topics in complex analysis, World Scientific, Singapore 1996, 136-142 (1997; Zbl 0884.53015).NEWLINENEWLINEFor the entire collection see [Zbl 0971.00014].
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