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

DOI10.1515/advgeom-2017-0061zbMath1406.53056arXiv1604.04934OpenAlexW2963715995WikidataQ115237040 ScholiaQ115237040MaRDI QIDQ1629380

Silvio Reggiani

Publication date: 11 December 2018

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.04934

zbMATH Keywords

naturally reductive spacedistribution of symmetryindex of symmetry, unimodular Lie group

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Differential geometry of symmetric spaces (53C35)

Related Items (4)

Homogeneous Riemannian manifolds with non-trivial nullity ⋮ Isometry groups of three-dimensional Lie groups ⋮ The distribution of symmetry of a naturally reductive nilpotent Lie group ⋮ Manifolds admitting a metric with co-index of symmetry 4

Cites Work

• Compact homogeneous Riemannian manifolds with low coindex of symmetry
• The space of left-invariant metrics on a Lie group up to isometry and scaling
• Curvatures of left invariant metrics on Lie groups
• Degenerations of Lie algebras and geometry of Lie groups
• Classification of left-invariant metrics on the Heisenberg group
• The isometry groups of simply connected 3-dimensional unimodular Lie groups
• The index of symmetry of compact naturally reductive spaces
• The index of symmetry of a flag manifold
• Holonomy and the Lie Algebra of Infinitesimal Motions of a Riemannian Manifold
• Curvature invariants, Killing vector fields, connections and cohomogeneity
• Left invariant metrics and curvatures on simply connected three-dimensional Lie groups

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