Closed geodesics on manifolds with infinite Abelian fundamental group (Q797162)
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scientific article; zbMATH DE number 3868163
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Closed geodesics on manifolds with infinite Abelian fundamental group |
scientific article; zbMATH DE number 3868163 |
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Closed geodesics on manifolds with infinite Abelian fundamental group (English)
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1984
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It is proved that the number of geometrically distinct closed geodesics on a compact Riemannian manifold with fundamental group \(\pi_ 1={\mathbb{Z}}\) grows at least like the prime numbers. In particular, there are infinitely many closed geodesics on such manifolds
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closed geodesics
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compact Riemannian manifold
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fundamental group
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