Refined Chern conjecture on isoparametric minimal hypersurfaces

Let $M^n$ be a closed immersed minimal hypersurface of the sphere $\mathbb{S}^{n+1}$ with constant scalar curvature. Refined Chern conjecture. Then $M^n$ is isoparametric.

The text presents this as a refinement of Chern's conjecture and does not state whether it has been resolved.