Polar actions on symmetric spaces of higher rank

Details Polar actions on symmetric spaces of higher rank Polar actions on symmetric spaces of higher rank

2011-08-16

arxiv.org/abs/1108.3256v2

Mathematics

Differential Geometry

7 pages; A. Lytchak added as author; shorter, conceptual proof

Scientific paper

We show that polar actions of cohomogeneity two on simple compact Lie groups of higher rank, endowed with a biinvariant Riemannian metric, are hyperpolar. Combining this with a recent result of the second-named author, we are able to prove that polar actions (of arbitrary cohomogeneity) induced by reductive algebraic subgroups in the isometry group of an irreducible Riemannian symmetric space of higher rank (compact or non-compact) are hyperpolar.

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