Gráficos compactos com curvatura média de segunda ordem constante sobre a esfera - Silva Filho, João Francisco da (2009)
The purpose of this dissertation is to desire a formula for the operator Lr(g) = div(Pr gradient g) of a new support function g, defined over a hypersurface Mn in a Riemannian space form Mc n +1, and to show that a compact smooth starshaped hypersurface Σn in the Euclidean sphere Sn+1,whose second symmetric function S2 is positive and constant must be a geodesic sphere Sn (p). This generalizes a result obtained by Jellett [9] in 1853 for such surfaces in Euclidean space R3.