Complete Hypersurfaces with Constant Mean Curvature in a Unit Sphere

By investigating hypersurfaces Mn in the unit sphere Sn+1(1) with constant mean curvature and with two distinct principal curvatures, we give a characterization of the torus S1(a) × \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S^{n-1}(\sqrt{1-a^2})$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a^2=\frac{2+nH^2\pm\sqrt{n^2H^4+4(n-1)H^2}}{2n(1+H^2)}$\end{document}. We extend recent results of Hasanis et al. [5] and Otsuki [10].