Polar actions with a fixed point

Details Polar actions with a fixed point Polar actions with a fixed point

2010-01-20

arxiv.org/abs/1001.3535v1

Mathematics

Differential Geometry

Scientific paper

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar and the section is the tangent space of an embedded totally geodesic submanifold. We apply this to obtain a classification of polar actions with a fixed point on symmetric spaces.

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