Sobre a aplicação de Gauss para hipersuperfícies com curvatura de ordem superior constante em esferas - Baltazar, Halyson Irene (2009)
In this work we will consider connected, complete and orientable hyper-surface of the unit euclidean sphere Sn+1 with constant positive high order curvature. We will prove that under certain geometric conditions, if the image of the Gauss mapping of M is contained in a closed hemisphere, then M is atotally umbilic hypersurface of Sn+1.