On the Second Pinching Theorem for Willmore Hypersurfaces in a Sphere

In this paper, we consider n-dimensional compact Willmore hypersurface in a unit sphere. We prove a pinching theorem of ρ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho ^2$$\end{document}, which is defined as ρ2=S-nH2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho ^2=S-nH^2$$\end{document}, for n-dimensional compact Willmore hypersurface with constant mean curvature and constant scalar curvature, where H denotes the mean curvature and S the squared norm of the second fundamental form of this hypersurface.