On the conformal class of the standard metric on the product \(S^2 \times S^2\) (Q2713914)
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scientific article; zbMATH DE number 1603174
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the conformal class of the standard metric on the product \(S^2 \times S^2\) |
scientific article; zbMATH DE number 1603174 |
Statements
10 June 2001
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Hopf conjecture
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positive sectional curvature
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On the conformal class of the standard metric on the product \(S^2 \times S^2\) (English)
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The famous Hopf conjecture asserts that there is no positively curved metric on the product \(M=S^2 \times S^2\) of two two-dimensional spheres. The authors consider a particular case of a Riemannian metric on \(M\) in which the metric is conformally equivalent to the standard product metric on \(M\). They show that, for every standard two-torus in \(M\), such a metric has a plane of nonpositive curvature which is tangent to this torus.
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