Sharp pinching theorems for complete submanifolds in the sphere

Marco Magliaro, Luciano Mari, Fernanda Roing +1

We prove that every complete, minimally immersed submanifold $f{M}^n\to {\mathbb{S}}^{n+p}$ whose second fundamental form satisfies $|A{|}^2\le np/(2p-1)$, is either totally geodesi…