Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations
We prove that the group of isometries preserving a metric foliation on a closed Alexandrov space is a closed subgroup of the isometry group of . We obtain a sharp upper bound for the dimension of this subgroup and show that, when equality holds, the foliations that realize this upper bound are indu...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214182 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations. Diego Corro and Fernando Galaz-García. SIGMA 21 (2025), 106, 23 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713469050028032 |
|---|---|
| author | Corro, Diego Galaz-García, Fernando |
| author_facet | Corro, Diego Galaz-García, Fernando |
| citation_txt | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations. Diego Corro and Fernando Galaz-García. SIGMA 21 (2025), 106, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove that the group of isometries preserving a metric foliation on a closed Alexandrov space is a closed subgroup of the isometry group of . We obtain a sharp upper bound for the dimension of this subgroup and show that, when equality holds, the foliations that realize this upper bound are induced by fiber bundles whose fibers are round spheres or projective spaces. As a corollary, singular Riemannian foliations that realize the upper bound are induced by smooth fiber bundles whose fibers are round spheres or projective spaces.
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| first_indexed | 2026-03-19T22:19:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214182 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T22:19:02Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Corro, Diego Galaz-García, Fernando 2026-02-20T07:53:46Z 2025 Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations. Diego Corro and Fernando Galaz-García. SIGMA 21 (2025), 106, 23 pages 1815-0659 2020 Mathematics Subject Classification: 53C12; 53C20; 53C21; 53C23; 53C24; 51K10 arXiv:2407.03534 https://nasplib.isofts.kiev.ua/handle/123456789/214182 https://doi.org/10.3842/SIGMA.2025.106 We prove that the group of isometries preserving a metric foliation on a closed Alexandrov space is a closed subgroup of the isometry group of . We obtain a sharp upper bound for the dimension of this subgroup and show that, when equality holds, the foliations that realize this upper bound are induced by fiber bundles whose fibers are round spheres or projective spaces. As a corollary, singular Riemannian foliations that realize the upper bound are induced by smooth fiber bundles whose fibers are round spheres or projective spaces. We thank Alexander Lytchak and Marco Radeschi for helpful comments on a preliminary version of this article. We thank the organizers of the IV joint meeting of RSME and SMM, and the Universidad Politécnica de Valencia, for their hospitality while this manuscript was finished. We thank the anonymous referees for suggestions that improved both clarity and accuracy. In particular, we are grateful to one of the referees for observations that helped strengthen Theorems A and B and simplify their proofs, for pointing out the argument in the proof of Proposition 2.23, and for proposing the question highlighted in Remark 1.5. D. Corro was supported in part by UNAM-DGAPA Postdoctoral fellowship of the Institute of Mathematics, and by the DFG (grant CO 2359/1-1, Priority Programme SPP2026 “Geometry at Infinity”), and by a UKRI Future Leaders Fellowship [grant number MR/W01176X/1; PI: J Harvey]. F. Galaz-Garc´ıa was supported in part by the DFG (grant GA 2050 2-1, Priority Programme SPP2026 “Geometry at Infinity”). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations Article published earlier |
| spellingShingle | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations Corro, Diego Galaz-García, Fernando |
| title | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations |
| title_full | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations |
| title_fullStr | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations |
| title_full_unstemmed | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations |
| title_short | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations |
| title_sort | myers-steenrod theorems for metric and singular riemannian foliations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214182 |
| work_keys_str_mv | AT corrodiego myerssteenrodtheoremsformetricandsingularriemannianfoliations AT galazgarciafernando myerssteenrodtheoremsformetricandsingularriemannianfoliations |