Totally umbilic surfaces in homogeneous 3-manifolds

By Rabah Souam, Eric Toubiana. 2006

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e90bf186791abf5536aeeddc05ca91e041a562b3