Prescribed Riemannian Symmetries
Given a smooth free action of a compact connected Lie group on a smooth compact manifold , we show that the space of -invariant Riemannian metrics on whose automorphism group is precisely is open and dense in the space of all -invariant metrics, provided the dimension of is ''sufficien...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211319 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Prescribed Riemannian Symmetries. Alexandru Chirvasitu. SIGMA 17 (2021), 030, 17 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862628520893612032 |
|---|---|
| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| citation_txt | Prescribed Riemannian Symmetries. Alexandru Chirvasitu. SIGMA 17 (2021), 030, 17 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Given a smooth free action of a compact connected Lie group on a smooth compact manifold , we show that the space of -invariant Riemannian metrics on whose automorphism group is precisely is open and dense in the space of all -invariant metrics, provided the dimension of is ''sufficiently large'' compared to that of . As a consequence, it follows that every compact connected Lie group can be realized as the automorphism group of some compact connected Riemannian manifold; this recovers prior work by Bedford-Dadok and Saerens-Zame under less stringent dimension conditions. Along the way, we also show, under less restrictive conditions on both dimensions and actions, that the space of -invariant metrics whose automorphism groups preserve the -orbits is dense δ in the space of all -invariant metrics.
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| first_indexed | 2026-03-14T17:00:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211319 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T17:00:27Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chirvasitu, Alexandru 2025-12-29T11:10:23Z 2021 Prescribed Riemannian Symmetries. Alexandru Chirvasitu. SIGMA 17 (2021), 030, 17 pages 1815-0659 2020 Mathematics Subject Classification: 53B20; 58D17; 58D19; 57S15 arXiv:2008.10072 https://nasplib.isofts.kiev.ua/handle/123456789/211319 https://doi.org/10.3842/SIGMA.2021.030 Given a smooth free action of a compact connected Lie group on a smooth compact manifold , we show that the space of -invariant Riemannian metrics on whose automorphism group is precisely is open and dense in the space of all -invariant metrics, provided the dimension of is ''sufficiently large'' compared to that of . As a consequence, it follows that every compact connected Lie group can be realized as the automorphism group of some compact connected Riemannian manifold; this recovers prior work by Bedford-Dadok and Saerens-Zame under less stringent dimension conditions. Along the way, we also show, under less restrictive conditions on both dimensions and actions, that the space of -invariant metrics whose automorphism groups preserve the -orbits is dense δ in the space of all -invariant metrics. This work is partially supported by NSF grants DMS-1801011 and DMS-2001128. I am indebted to the anonymous referees for numerous suggestions contributing to the improved quality of the initial draft. In particular, I would have remained unacquainted with [3, 32] were it not for one of the referee reports. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Prescribed Riemannian Symmetries Article published earlier |
| spellingShingle | Prescribed Riemannian Symmetries Chirvasitu, Alexandru |
| title | Prescribed Riemannian Symmetries |
| title_full | Prescribed Riemannian Symmetries |
| title_fullStr | Prescribed Riemannian Symmetries |
| title_full_unstemmed | Prescribed Riemannian Symmetries |
| title_short | Prescribed Riemannian Symmetries |
| title_sort | prescribed riemannian symmetries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211319 |
| work_keys_str_mv | AT chirvasitualexandru prescribedriemanniansymmetries |