Argentina
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The index of symmetry of three-dimensional Lie groups with a left-invariant metric
Fecha
2018-10Registro en:
Reggiani, Silvio Nicolás; The index of symmetry of three-dimensional Lie groups with a left-invariant metric; De Gruyter; Advances In Geometry; 18; 4; 10-2018; 395-404
1615-7168
1615-715X
CONICET Digital
CONICET
Autor
Reggiani, Silvio Nicolás
Resumen
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.