Totally umbilic surfaces in homogeneous 3-manifolds

Rabah Souam; Eric Toubiana

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Totally umbilic surfaces in homogeneous 3-manifolds

Rabah Souam·Eric Toubiana

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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.

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Rabah Souam, Eric Toubiana. 2008-06-20. Totally umbilic surfaces in homogeneous 3-manifolds. https://arxiv.org/abs/math/0604391

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