On closed minimal hypersurfaces with constant scalar curvature in $$\mathbb{S}^7$$

We consider minimal closed hypersurfaces \({M \subset \mathbb{S}^7(1)}\) with constant scalar curvature. We prove that if M fulfills particular additional assumptions, then it is isoparametric. This gives a partial answer to the question made by S.-S. Chern about the pinching of the scalar curvature for closed minimal hypersurfaces in dimension 6.