Totally umbilic surfaces in homogeneous 3-manifolds

Rabah Souam; Eric Toubiana

Totally umbilic surfaces in homogeneous 3-manifolds

Differential Geometry 2008-06-20 v2

Authors: 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 $H^2 \times R$ , $S^2 \times R$ and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.

Keywords

totally umbilic surfaces homogeneous 3-manifolds thurston geometries berger spheres sol group classification nonexistence

Cite

@article{arxiv.math/0604391,
  title  = {Totally umbilic surfaces in homogeneous 3-manifolds},
  author = {Rabah Souam and Eric Toubiana},
  journal= {arXiv preprint arXiv:math/0604391},
  year   = {2008}
}

Comments

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

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