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...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2025
Main Authors: Corro, Diego, Galaz-García, Fernando
Format: Article
Language:English
Published: Інститут математики НАН України 2025
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/214182
Tags: Add Tag
No Tags, Be the first to tag this record!
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

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Description
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.
ISSN:1815-0659