Totally umbilic surfaces in homogeneous 3-manifolds

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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.
28 pages, v2 : corrected typos, new section added. To appear in Commentarii Math. Helvet

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Differential Geometry, 53C30, 53B25

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http://salesiana.dossiersoluciones.com/handle/123456789/163270

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604391
 http://arxiv.org/abs/math/0604391

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arXiv