Three-dimensional manifolds having metrics with the same geodesics. (Q1398217)
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scientific article; zbMATH DE number 1956008
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Three-dimensional manifolds having metrics with the same geodesics. |
scientific article; zbMATH DE number 1956008 |
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Three-dimensional manifolds having metrics with the same geodesics. (English)
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29 July 2003
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The author proves that if two Riemannian metrics have the same geodesics on a closed three-dimensional manifold which is homeomorphic neither to a lens space nor to a Seifert manifold with zero Euler number, then the metrics are proportional.
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Geodesic equivalence
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Projectively equivalent metrics
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Projective connection
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Integrable system
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Separation of variables
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Geodesic rigidity
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Liouville metric
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Stäckel system
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Obstructions to integrability
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Local product structure
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Lens space
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