Special Issue: Celebrating the 75th Birthday of V.V. Kozlov (Issue Editors: Sergey Bolotin, Vladimir Dragović, and Dmitry Treschev)

The Lorentzian Anti-de Sitter Plane

Anton Z. Ali^a, Yuri L. Sachkov<sup>b

a</sup> Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia
^b Ailamazyan Program Systems Institute RAS, RUDN University, 152020 Pereslavl-Zalessky, Russia

Abstract: In this paper the two-dimensional Lorentzian problem on the anti-de Sitter plane is studied. Using methods of geometric control theory and differential geometry, we describe the reachable set, investigate the existence of Lorentzian length maximizers, compute extremal trajectories, construct an optimal synthesis, characterize Lorentzian distance and spheres, and describe the Lie algebra of Killing vector fields.

Keywords: Lorentzian geometry, geometric control theory, optimal control

MSC: 53C50, 49K15

Received: 21.04.2025
Accepted: 15.07.2025

Language: English

DOI: 10.1134/S1560354725040045