Polar action

In mathematics, a polar action is a proper and isometric action of a Lie group G on a complete Riemannian manifold M for which there exists a complete submanifold Σ that meets all the orbits and meets them always orthogonally; such a submanifold is called a section. A section is necessarily totally geodesic. If the sections of a polar action are flat with respect to the induced metric, then the action is called hyperpolar.