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arXiv · 1302.2876

The classification of totally umbilical surfaces in homogeneous 3-manifolds

José M. Manzano·Rabah Souam
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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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José M. Manzano, Rabah Souam. 2013-02-14. The classification of totally umbilical surfaces in homogeneous 3-manifolds. https://doi.org/10.1007/s00209-014-1381-8

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