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 |
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World Scientific Publishing
2024
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| _version_ | 1811140413456646144 |
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| author | Papazoglou, P Swenson, E |
| author_facet | Papazoglou, P Swenson, E |
| author_sort | Papazoglou, P |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-09-25T04:21:35Z |
| format | Journal article |
| id | oxford-uuid:1825ca69-03ef-4ca4-8447-1ab26f834a8f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:21:35Z |
| publishDate | 2024 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:1825ca69-03ef-4ca4-8447-1ab26f834a8f2024-08-14T12:38:23ZPeriodic geodesics in singular spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1825ca69-03ef-4ca4-8447-1ab26f834a8fEnglishSymplectic ElementsWorld Scientific Publishing2024Papazoglou, PSwenson, EWe 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. |
| spellingShingle | Papazoglou, P Swenson, E Periodic geodesics in singular spaces |
| title | Periodic geodesics in singular spaces |
| title_full | Periodic geodesics in singular spaces |
| title_fullStr | Periodic geodesics in singular spaces |
| title_full_unstemmed | Periodic geodesics in singular spaces |
| title_short | Periodic geodesics in singular spaces |
| title_sort | periodic geodesics in singular spaces |
| work_keys_str_mv | AT papazogloup periodicgeodesicsinsingularspaces AT swensone periodicgeodesicsinsingularspaces |