On the existence of closed geodesics on noncompact Riemannian manifolds (Q1210420)
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scientific article; zbMATH DE number 179212
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of closed geodesics on noncompact Riemannian manifolds |
scientific article; zbMATH DE number 179212 |
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On the existence of closed geodesics on noncompact Riemannian manifolds (English)
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8 August 1993
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The main result of the paper assures the existence of a closed geodesic on a complete noncompact Riemannian manifold \(M\) provided that (i) for some integer \(q > 2\dim M\) and some field \(k\) the \(q\)-th homology group with coefficients in \(k\) of the free loop space of \(M\) does not vanish and (ii) the sectional curvature of \(M\) is asymptotically nonpositive.
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closed geodesic
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complete noncompact Riemannian manifold
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