The index of symmetry for a left-invariant metric on a solvable three-dimensional Lie group

2021/03/29 by Robert May, Robert D. May, Robert M. May +1 · 1 citation
Mathematics · Physics and Astronomy · #22E15 (Primary) 22E25 #22E99 (Secondary) #Advanced Differential Geometry Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:22E15 #msc:22E25 #msc:22E99

paper · pdf · doi:10.48550/arxiv.2103.15789

25 pages

openalex publication_date 2021/03/29 · arxiv created 2021/04/17 · arxiv updated 2021/04/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We find the index of symmetry for all solvable three-dimensional Lie groups with a left-invariant metric. When combined with the work of Reggiani on unimodular three-dimensional Lie groups, the index of symmetry is then known for all three-dimensional Lie groups with a left-invariant metric. Similar to the unimodular case, for every solvable three-dimensional Lie algebra there is at least one left-invariant metric for which the index of symmetry is positive. Also, the index is never equal to 2.

Citations

• Curvatures of left invariant metrics on lie groups

Cited by

• The distribution of symmetry of Lorentzian naturally reductive nilmanifolds

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