Lange, Christian (2020). On metrics on 2-orbifolds all of whose geodesics are closed. J. Reine Angew. Math., 758. S. 67 - 95. BERLIN: WALTER DE GRUYTER GMBH. ISSN 1435-5345
Full text not available from this repository.Abstract
We show that the periods and the topology of the space of closed geodesics on a Riemannian 2-orbifold all of whose geodesics arc closed depend, up to scaling, only on the orbifold topology and compute it. In the manifold case we recover the fact proved by Gromoll, Grove and Pries that all prime geodesics have the same length, without referring to the existence of simple geodesics. We partly strengthen our result in terms of conjugacy of contact forms and explain how to deduce rigidity on the projective plane based on a systolic inequality due to Pu.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-352385 | ||||||||
| DOI: | 10.1515/crelle-2017-0050 | ||||||||
| Journal or Publication Title: | J. Reine Angew. Math. | ||||||||
| Volume: | 758 | ||||||||
| Page Range: | S. 67 - 95 | ||||||||
| Date: | 2020 | ||||||||
| Publisher: | WALTER DE GRUYTER GMBH | ||||||||
| Place of Publication: | BERLIN | ||||||||
| ISSN: | 1435-5345 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/35238 |
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