Planes without conjugate points (Q1057518)
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scientific article; zbMATH DE number 3897768
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Planes without conjugate points |
scientific article; zbMATH DE number 3897768 |
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Planes without conjugate points (English)
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1985
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The authors prove the following theorem. Suppose g to be a Riemannian metric on \({\mathbb{R}}^ 2\) which differs from the Euclidean metric only on a compact set. If g has no conjugate points, then g is isometric to the Euclidean metric. The proof rests on E. Hopf's theorem that a two- dimensional torus without conjugate points must be flat.
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Riemannian metric on \({\mathbb{R}}^ 2\)
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conjugate points
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geodesics
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