English

Polar actions on symmetric spaces

Differential Geometry 2011-01-12 v2

Abstract

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry group and rank greater than one. In particular we show that these actions are hyperpolar, i.e. the sections are flat.

Keywords

Cite

@article{arxiv.math/0506312,
  title  = {Polar actions on symmetric spaces},
  author = {Andreas Kollross},
  journal= {arXiv preprint arXiv:math/0506312},
  year   = {2011}
}

Comments

45 pages; erroneous Proposition 3.4 deleted; other minor changes and typos corrected; results remain unchanged

R2 v1 2026-07-22T17:20:47.045Z