Totally umbilic surfaces in homogeneous 3-manifolds

Abstract

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.

28 pages, v2 : corrected typos, new section added. To appear in Commentarii Math. Helvet