Chern's gap conjecture for minimal submanifolds of spheres

Let $M^n$ be a compact minimal submanifold in the sphere $S^{n+m}$, and let $B$ denote its second fundamental form. Assume that the squared norm $|B|^2$ is constant.

Chern's conjecture. The value of $|B|^2$ must lie in a discrete subset of $\mathbb{R}$.

This conjecture is a proposed intrinsic rigidity principle for compact minimal submanifolds of spheres, extending the phenomenon in Simons' rigidity theorem. It was raised by S. S. Chern and listed by S. T. Yau among the 120 open problems in differential geometry; its general status remains open.