Rigidity theorems of Clifford Torus - SOUSA JR. LUIZ A. M. (Anais da Academia Brasileira de Ciências, 2001)
Let M be an n-dimensional closed minimally immersed hypersurface in the unit sphere Sn + 1. Assume in addition that M has constant scalar curvature or constant Gauss-Kronecker curvature. In this note we announce that if M has (n - 1) principal curvatures with the same sign everywhere, then M is isometric to a Clifford Torus .