Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere

In this paper, we give a characterization of tori \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S^{1} {\left( {{\sqrt {\frac{{nr + 2 - n}} {{nr}}} }} \right)} \times S^{{n - 1}} {\left( {{\sqrt {\frac{{n - 2}} {{nr}}} }} \right)} $$ \end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S^{m} {\left( {{\sqrt {\frac{m} {n}} }} \right)} \times S^{{n - m}} {\left( {{\sqrt {\frac{{n - m}} {n}} }} \right)} $$\end{document}. Our result extends the result due to Li (1996) on the condition that M is an n-dimensional complete hypersurface in Sn+1 with two distinct principal curvatures.