  In 1951, H. Hopf proved that the only surfaces, homeomorphic to the sphere,
with constant mean curvature in the Euclidean space are the round (geometrical)
spheres. In this paper we survey some contributions of Renato Tribuzy to
generalize the result of Hopf as well as some recent results of the authors
using these techniques for shrinking solitons of curvature flows and for
surfaces in three-dimensional warped product manifolds, specially the de
Sitter-Schwarzschild and Reissner-Nordstrom manifolds.
