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

2016/04/17 by Silvio Reggiani, Reggiani, Silvio · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1604.04934

Abstract

We determine the index of symmetry of 3-dimensional unimodular Lie groups\nwith a left-invariant metric. In particular, we prove that every 3-dimensional\nunimodular Lie group admits a left-invariant metric with positive index of\nsymmetry. We also study the geometry of the quotients by the so-called\nfoliation of symmetry, and we explain in what cases the group fibers over a\n2-dimensional space of constant curvature.\n

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• The distribution of symmetry of Lorentzian naturally reductive nilmanifolds

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