On the average of the scalar curvature of minimal hypersurfaces of spheres with low stability index

Abstract

In this paper we show that if the stability index of $M$ is equal to $n+2$, then the average of the function $|A|^2$ is less than or equal to $n-1$. Moreover, if this average is equal to $n-1$, then $M$ must be isometric to a Clifford minimal hypersurface.