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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214182 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Myers-Steenrod Theorems for Metric and Singular Riemannian Foliations. Diego Corro and Fernando Galaz-García. SIGMA 21 (2025), 106, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |