Grove–Ziller conjecture on hyperbolic sections and rational hyperbolicity

Let $M$ be a compact, simply connected manifold with a polar action by a compact group $G$, meaning an isometric action admitting a section $S$ with $\dim S=\dim M/G$ that meets all orbits perpendicularly. A section is called hyperbolic when it has hyperbolic geometry. Grove–Ziller conjecture. If the section is hyperbolic, then $M$ is rationally hyperbolic. This conjecture proposes the sharp converse to known rational-ellipticity results for polar actions with flat or spherical sections; the source does not state whether it has been resolved.