Non-existence of exceptional orbits under polar actions on Hilbert spaces
Differential Geometry
2023-09-01 v2
Abstract
We prove that any polar action on a separable Hilbert space by a connected Hilbert Lie group does not have exceptional orbits. This generalizes a result of Berndt, Console and Olmos in the finite dimensional Euclidean case. As an application, we give a simple geometric proof of the fact that any hyperpolar action on a simply connected compact Riemannian symmetric space by a connected Lie group does not have exceptional orbits.
Keywords
Cite
@article{arxiv.2307.02782,
title = {Non-existence of exceptional orbits under polar actions on Hilbert spaces},
author = {Masahiro Morimoto},
journal= {arXiv preprint arXiv:2307.02782},
year = {2023}
}
Comments
9 pages. Added some references, added Section 2 and revised the introduction