Lorentzian distance on the Lobachevsky plane
Yu.L. Sachkov
TL;DR
This paper investigates the geometric properties of Lorentzian structures on a specific 2D Lie group, analyzing curvature, distance, and isometries to deepen understanding of Lorentzian geometry in this context.
Contribution
It provides a detailed analysis of Lorentzian geometry on the Lobachevsky plane, including curvature, distance, and symmetry properties, which were not previously comprehensively studied.
Findings
Description of sectional curvature and attainable sets
Characterization of Lorentzian length maximizers and distance
Identification of infinitesimal isometries
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.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research