Isometries between leaf spaces

2011/11/26 by Marcos M. Alexandrino, Marco Radeschi, Alexandrino, Marcos M. +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1111.6178

openalex publication_date 2011/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that an isometry between orbit spaces of two proper isometric actions is smooth if it preserves the codimension of the orbits or if the orbit spaces have no boundary. In other words, we generalize Myers-Steenrod's theorem for orbit spaces. These results are proved in the more general context of singular Riemannian foliations.

Cited by

• Manifold submetries from compact homogeneous spaces

Related

• Smoothness of isometric flows on orbit spaces and applications to the theory of foliations
• On smoothness of isometries between orbit spaces
• Leaf Space Isometries of Singular Riemannian Foliations and Their Spectral Properties
• The Boundary Conjecture for Leaf Spaces
• Proper isometric actions