Polar actions on certain principal bundles over symmetric spaces of compact type

Details Polar actions on certain principal bundles over symmetric spaces of compact type Polar actions on certain principal bundles over symmetric spaces of compact type

2010-03-15

arxiv.org/abs/1003.2956v3

Proc. Amer. Math. Soc. 139 (2011), 2249-2255

Mathematics

Differential Geometry

7 pages; some minor changes

Scientific paper

We study polar actions with horizontal sections on the total space of certain principal bundles $G/K\to G/H$ with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

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