Totally umbilic surfaces in homogeneous 3-manifolds
  We discuss existence and classification of totally umbilic surfaces in the model geometries of Thurston and the Berger spheres. We classify such surfaces in $H^2 \times R$, $S^2 \times R$ and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms. 
Rabah Souam (IMJ), Eric Toubiana (IMJ)