JournalscmhVol. 84 , No. 3DOI 10.4171/cmh/177

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

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.