Tang's conjecture on nonnegative curvature of isoparametric leaves

Let $M$ be an isoparametric hypersurface or a focal submanifold of the unit sphere $\mathbb{S}^n$. Tang's conjecture. Every such isoparametric hypersurface and focal submanifold admits a Riemannian metric of nonnegative sectional curvature. The source presents this as an interesting problem and notes a tension with Hitchin's obstruction to positive scalar curvature on certain exotic spheres; the conjecture remains open.