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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2025
Hauptverfasser: Corro, Diego, Galaz-García, Fernando
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2025
Online Zugang: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
Zitieren: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
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Zusammenfassung: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.
ISSN:1815-0659