6 problems

Let $M$ be a compact symmetric space of rank bigger than one, and let a compact Lie group act polarly on $M$. Hyperpolarity conjecture. The action is hyperpolar. This extends the p…

Let a compact Lie group act smoothly and isometrically on a simply connected compact manifold of nonnegative curvature. The action is irreducible when its associated reflection gro…

Let $M$ be a simply connected polar manifold, meaning a Riemannian manifold with an isometric polar group action, and suppose that $M$ is hyperbolic in the sense that its section h…

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…

Let $M$ be an irreducible compact Riemannian symmetric space of rank greater than one, and let a connected Lie group act nontrivially and polarly on $M$. A polar action is one admi…

Let a compact Lie group $G$ act isometrically on a Riemannian manifold $M$, and suppose that the distribution of normal spaces to the regular $G$-orbits is integrable. Palais–Terng…