Polar actions on Hermitian and quaternion-Kähler symmetric spaces

Details Polar actions on Hermitian and quaternion-Kähler symmetric spaces Polar actions on Hermitian and quaternion-Kähler symmetric spaces

2006-12-18

arxiv.org/abs/math/0612479v2

Mathematics

Differential Geometry

22 pages; corrected typos; minor correction of Lemma 4.13

Scientific paper

We analyze polar actions on Hermitian and quaternion-K\"ahler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classification of polar actions on Hermitian symmetric spaces. In the second part we prove that polar actions on Wolf spaces are quaternion-coisotropic and that isometric actions on these spaces admit an orbit of special type, analogous to the existence of a complex orbit for an isometric action on a compact homogeneous simply-connected K\"ahler manifold.

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