Lorentzian distance on the Lobachevsky plane

2023/07/15 by Yu. L. Sachkov, Sachkov, Yu. L. · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2307.07706

openalex publication_date 2023/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Left-invariant Lorentzian structures on the 2D solvable non-Abelian Lie group are studied. Sectional curvature, attainable sets, Lorentzian length maximizers, distance, spheres, and infinitesimal isometries are described.

Cited by

• Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group
• Sectional curvature and structure functions of a two-dimensional Lorentzian manifold
• Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups

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