Rigidity of Three-Dimensional Self-Shrinkers with Constant Norm of the Second Fundamental Form

Shanlin Guan, Yuhang Zhao

Let $X:M^3\to {\mathbb{R}}^4$ be a complete, connected self-shrinker without boundary, and suppose that the squared norm $S$ of its second fundamental form is constant. We prove that $S=0$ or…