Sobre a aplicação de Gauss de hipersuperficies com curvatura escalar constante em esferas - Macedo, Elivaldo Rodrigues (2006)
The purpose of the dissertation is to characterize hypersurfaces in the Euclidean sphere with constant mean curvature of higher order. We prove that if M is a Riemannian manifold of dimension n and the image of the Gaussian map of M is contained in a closed hemisphere of the sphere of dimension n+1 then M is totally umbilical.