The index of symmetry of three-dimensional Lie groups with a left-invariant metric

Silvio Reggiani

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arXiv · 1604.04934

The index of symmetry of three-dimensional Lie groups with a left-invariant metric

Silvio Reggiani

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Abstract

We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry, and we explain in what cases the group fibers over a 2-dimensional space of constant curvature.

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Silvio Reggiani. 2016-04-17. The index of symmetry of three-dimensional Lie groups with a left-invariant metric. https://arxiv.org/abs/1604.04934

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