Sub-Riemannian distance on the Lie group SO₀(2,1)

2015/07/20 by V. N. Berestovskiĭ, V. Berestovskii, Berestovskii, V. +3
Mathematics · Physics and Astronomy · #22E30 #49J15 #53C17 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG #msc:22E30 #msc:49J15 #msc:53C17

paper · pdf · doi:10.48550/arxiv.1507.05554

15 pages, 0 figures

openalex publication_date 2015/07/20 · arxiv created 2015/07/21 · arxiv updated 2015/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A left-invariant sub-Riemannian metric d on the shortened Lorentz group SO₀(2,1) under the condition that d is right-invariant relative to the orthogonal Lie subgroup 1⊗ SO(2) is studied. The distance between arbitrary two elements, the cut locus (as the union of the subgroup 1⊗ SO(2) with the antipodal set to the submanifold of symmetric matrices in the open solid torus SO₀(2,1)), and the conjugate set for the unit are found for (SO₀(2,1),d).

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