The Second Gap and Rigidity in Chern's Conjecture with Constant Cubic Trace

Jianquan Ge, Huixin Tan, Wenjiao Yan +1

Let $M^n\subset {\mathbb{S}}^{n+1}(1)$ be a closed minimal hypersurface with constant $S=|h{|}^2$ and constant $f_3=\mathrm{tr}{h}^3$, where $h$ is the shape operator. We prove tha…