English

The classification of totally umbilical surfaces in homogeneous 3-manifolds

Differential Geometry 2015-03-02 v2

Abstract

We obtain an exhaustive classification of totally umbilical surfaces in unimodular and non-unimodular simply-connected 3-dimensional Lie groups endowed with arbitrary left-invariant Riemannian metrics. This completes the classification of totally umbilical surfaces in homogeneous Riemannian 3-manifolds.

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Cite

@article{arxiv.1302.2876,
  title  = {The classification of totally umbilical surfaces in homogeneous 3-manifolds},
  author = {José M. Manzano and Rabah Souam},
  journal= {arXiv preprint arXiv:1302.2876},
  year   = {2015}
}

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21 pages