The polar-action conjecture for nonnegatively curved compact manifolds

A polar action is an isometric group action admitting a section, a submanifold meeting every orbit orthogonally. Let a compact simply connected manifold have nonnegative sectional curvature, and let the polar action on it be irreducible, meaning that it is not a product action. Polar-action conjecture. The action is equivariantly diffeomorphic to a polar action on a symmetric space. This would extend the classification of polar actions from positively curved manifolds to the nonnegative-curvature setting; the statement is presented as a conjectural expectation, and its general validity remains open.