Totally umbilic surfaces in homogeneous 3-manifolds
Rabah Souam, Eric Toubiana
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 H2 × R, S2 × R and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.
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