Torus cannot collapse to a segment (Q2309611)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Torus cannot collapse to a segment |
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Torus cannot collapse to a segment (English)
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1 April 2020
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It is shown that here is no sequence of \(2\)-tori equipped with smooth Riemannian metrics with Gauss curvature bounded from below, which converges in the Gromov-Hausdorff sense to a (non-degenerate) segment. In short, ``the torus cannot collpase to a segment.'' It is also shown that the flat Klein bottle collapses to a segment.
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torus
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Klein bottle
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collapsing Riemannian manifolds
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