Leafwise curvature conjecture for isoparametric foliations

Let $(N^n,\mathfrak{F})$ be an isoparametric foliation. Suppose its leaves have nonnegative or positive leafwise sectional curvature, $K_{\mathrm{sec}}^F\geqslant0$ or $K_{\mathrm{sec}}^F>0$, respectively, or nonnegative or positive leafwise Ricci curvature or leafwise scalar curvature. Leafwise curvature conjecture. Then the whole manifold $N$ admits a metric with the corresponding nonnegative or positive curvature. The conjecture generalizes Zhang's result for regular foliations with positive leafwise scalar curvature to singular isoparametric foliations; its general validity remains open.