Totally umbilic surfaces in homogeneous 3-manifolds

Rabah Souam (1) , Eric Toubiana (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Domaines: Géométrie différentielle [math.DG]

Rabah Souam, Eric Toubiana. Totally umbilic surfaces in homogeneous 3-manifolds. 2008. ⟨hal-00022419v2⟩