Sharp systolic inequalities for Riemannian and Finsler spheres of revolution
Trans. Amer. Math. Soc. 374 (2021), 1815-1845 We prove that the systolic ratio of a sphere of revolution $S$ does not exceed $\pi$ and equals $\pi$ if and only if $S$ is Zoll. More generally, we consider the rotationally symmetric Finsler metrics on a sphere of revolution which are defined by shifti...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Journal Article |
| Language: | English |
| Published: |
21-08-2018
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Trans. Amer. Math. Soc. 374 (2021), 1815-1845 We prove that the systolic ratio of a sphere of revolution $S$ does not
exceed $\pi$ and equals $\pi$ if and only if $S$ is Zoll. More generally, we
consider the rotationally symmetric Finsler metrics on a sphere of revolution
which are defined by shifting the tangent unit circles by a Killing vector
field. We prove that in this class of metrics the systolic ratio does not
exceed $\pi$ and equals $\pi$ if and only if the metric is Riemannian and Zoll. |
|---|---|
| AbstractList | Trans. Amer. Math. Soc. 374 (2021), 1815-1845 We prove that the systolic ratio of a sphere of revolution $S$ does not
exceed $\pi$ and equals $\pi$ if and only if $S$ is Zoll. More generally, we
consider the rotationally symmetric Finsler metrics on a sphere of revolution
which are defined by shifting the tangent unit circles by a Killing vector
field. We prove that in this class of metrics the systolic ratio does not
exceed $\pi$ and equals $\pi$ if and only if the metric is Riemannian and Zoll. |
| Author | Hryniewicz, Umberto L Salomão, Pedro A. S Bramham, Barney Abbondandolo, Alberto |
| Author_xml | – sequence: 1 givenname: Alberto surname: Abbondandolo fullname: Abbondandolo, Alberto – sequence: 2 givenname: Barney surname: Bramham fullname: Bramham, Barney – sequence: 3 givenname: Umberto L surname: Hryniewicz fullname: Hryniewicz, Umberto L – sequence: 4 givenname: Pedro A. S surname: Salomão fullname: Salomão, Pedro A. S |
| BackLink | https://doi.org/10.48550/arXiv.1808.06995$$DView paper in arXiv |
| BookMark | eNotz0FPwyAYxnEOetC5D7CTfIFWyoDC0SxOTZqY6O7NW3jJSDqo0C3u26vT03P550l-t-QqpoiErBpWCy0le4D8FU51o5mumTJG3pDuYw95ouVc5jQGS0PEzyOMYQ5YqE-Zvgc8QIwBIoXo6DbEMmKmZdpj_kmSpxlPaTzOIcU7cu1hLLj83wXZbZ92m5eqe3t-3Tx2FahWVsoPAq01rTdCKg9OamG5BCeUbJ03jLdoGXPIB9M0GrjmjDOnvWXceDesF-T-7_bC6accDpDP_S-rv7DW31_MSzE |
| ContentType | Journal Article |
| Copyright | http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| Copyright_xml | – notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| DBID | AKZ GOX |
| DOI | 10.48550/arxiv.1808.06995 |
| DatabaseName | arXiv Mathematics arXiv.org |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| ExternalDocumentID | 1808_06995 |
| GroupedDBID | AKZ GOX |
| ID | FETCH-LOGICAL-a675-6fb4ecc97f9456fad584c25ad4657df9027ec00de2b9118a282020d8fc029fdb3 |
| IEDL.DBID | GOX |
| IngestDate | Mon Jan 08 05:49:45 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a675-6fb4ecc97f9456fad584c25ad4657df9027ec00de2b9118a282020d8fc029fdb3 |
| OpenAccessLink | https://arxiv.org/abs/1808.06995 |
| ParticipantIDs | arxiv_primary_1808_06995 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-08-21 |
| PublicationDateYYYYMMDD | 2018-08-21 |
| PublicationDate_xml | – month: 08 year: 2018 text: 2018-08-21 day: 21 |
| PublicationDecade | 2010 |
| PublicationYear | 2018 |
| Score | 1.7087708 |
| SecondaryResourceType | preprint |
| Snippet | Trans. Amer. Math. Soc. 374 (2021), 1815-1845 We prove that the systolic ratio of a sphere of revolution $S$ does not
exceed $\pi$ and equals $\pi$ if and only... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Differential Geometry Mathematics - Dynamical Systems Mathematics - Symplectic Geometry |
| Title | Sharp systolic inequalities for Riemannian and Finsler spheres of revolution |
| URI | https://arxiv.org/abs/1808.06995 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdZ07T8MwEMdPpBMLAgEqT3lgtXCdh-MRQUMHBBJ06Bb5KUWCtEpoxcfn7ATBwmrf4vPjfif7_ga4UTjN2pWM6iI1FE9JTqXWnCovHPOpYbkLxcmLN_G8Kh_mQSaH_NTCqO6r2Q36wLq_nZVRXlPKPIGE8_Bk6_FlNVxORimu0f7XDhkzNv0JEtUhHIx0R-6G6TiCPdcew1MQRd6QoJkcRHgJct1QyohJKkFmJK-N-whfB6mWYF5Pqqbt311H-lDxjyZrTzq3G5fICSyr-fJ-QcdPDKhCFqeF1xl6SQovEVW8shjwDc-VzYpcWC8xK3SGMeu4xmOnVJgBIcDZ0hvGpbc6PYVJu27dFAjuLCm0ZgWzLEPKUUZJpB3hMWJLI4szmMah15tBp6IOXqmjV87_77qAfWSAoFJN-ewSJp_d1l1B0tvtdXT2N5uXfps |
| link.rule.ids | 228,230,782,887 |
| linkProvider | Cornell University |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Sharp+systolic+inequalities+for+Riemannian+and+Finsler+spheres+of+revolution&rft.au=Abbondandolo%2C+Alberto&rft.au=Bramham%2C+Barney&rft.au=Hryniewicz%2C+Umberto+L&rft.au=Salom%C3%A3o%2C+Pedro+A.+S&rft.date=2018-08-21&rft_id=info:doi/10.48550%2Farxiv.1808.06995&rft.externalDocID=1808_06995 |