A pinching theorem for minimal hypersurfaces in a sphere

Abstract.

We study compact minimal hypersurfaces M ⁿ in $S^{n+1}$ with two distinct principal curvatures and prove that if the squared norm S of the second fundamental form of M ⁿ satisfies $S \geqq n$, then $S \equiv n$ and M ⁿ is a minimal Clifford torus.