Publication date:
9 July 2017
Source:Advances in Mathematics, Volume 314
Author(s): Qintao Deng, Huiling Gu, Qiaoyu Wei
In this paper, we will prove that any closed minimal Willmore hypersurface $M^4$ of ${\mathbb{S}}^5$ with constant scalar curvature must be isoparametric. To be precise, $M^4$ is either an equatorial 4 sphere, a product of sphere ${\mathbb{S}}^2(\frac{\sqrt{2}}{2})\times {\mathbb{S}}^2(\frac{\sqrt{2}}{2})$ or a Cartan's minimal hypersurface. In particular, the value of the second fundamental form S can only be 0, 4, 12. This result strongly supports Chern's Conjecture.