A Curvature Gap for Minimal Submanifolds in Spheres

Fagui Li, Yuhang Zhao

Let $F:M^n\to\Sn^{n+q}(1)$ be a closed connected minimal immersion in the unit sphere with second fundamental form $h$, $n\ge 3$, $q\ge 2$, and $S=|h{|}^2$. We prove that if $M$ is not…