JournalscmhVol. 84, No. 3pp. 673–704

Totally umbilic surfaces in homogeneous 3-manifolds

  • Rabah Souam

    Institut Mathématiques de Jussieu, Paris, France
  • Eric Toubiana

    Institut Mathématiques de Jussieu, Paris, France
Totally umbilic surfaces in homogeneous 3-manifolds cover
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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 ℍ2 × ℝ, \mathbb{S}2 × ℝ and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.

Cite this article

Rabah Souam, Eric Toubiana, Totally umbilic surfaces in homogeneous 3-manifolds. Comment. Math. Helv. 84 (2009), no. 3, pp. 673–704

DOI 10.4171/CMH/177