The classification of totally umbilical surfaces in homogeneous 3-manifolds

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.

21 pages

References in corpus (1)

• On the classification of Killing submersions and their isometries

Cited by in corpus (2)

• Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: Minimization
• Polar actions on homogeneous 3-spaces