Total transversal scalar curvatures of Hopf \(\alpha\)-foliations (Q2758280)
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scientific article; zbMATH DE number 1679658
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Total transversal scalar curvatures of Hopf \(\alpha\)-foliations |
scientific article; zbMATH DE number 1679658 |
Statements
7 January 2004
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Hopf foliation on \(S^{3}\)
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total transversal scalar curvature
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foliated Riemannian manifold
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0.8966171
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0.8895273
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0.8869853
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0.88569355
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0.8853165
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0.8835707
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Total transversal scalar curvatures of Hopf \(\alpha\)-foliations (English)
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The author computes the total transversal scalar curvature of a Hopf \(\alpha\)-foliation \(\mathcal{F}^{\alpha}\) on the unit 3-sphere \(S^{3}\) and shows that it is equal to \(16 \pi ^{2}\) and it is independent on \(\alpha\). On the other hand, if \( \alpha , \beta \geq 1\) and \(\alpha \neq \beta\) , then the foliations \(\mathcal{F}^{\alpha}\) and \(\mathcal{F}^{\beta}\) are not isospectral.
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