Totally umbilic surfaces in homogeneous 3-manifolds

Research paper by Rabah Souam, Eric Toubiana

Indexed on: 20 Jun '08Published on: 20 Jun '08Published in: Mathematics - Differential Geometry


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.