Periodic geodesics in singular spaces
We extend the classical result of Lyusternik and Fet on the existence of closed geodesics to singular spaces. We show that if X is a compact geodesic metric space satisfying the CAT(κ) condition for some fixed κ>0 and πn(X)≠0 for some n>0 then X has a periodic geodesic. This condition is satis...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
World Scientific Publishing
2024
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| Summary: | We extend the classical result of Lyusternik and Fet on the existence of closed geodesics to singular spaces. We show that if X is a compact geodesic metric space satisfying the CAT(κ) condition for some fixed κ>0 and πn(X)≠0 for some n>0 then X has a periodic geodesic. This condition is satisfied for example by locally CAT(κ) manifolds. Our result applies more generally to compact locally uniquely geodesic spaces. |
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