Lorentzian problems on the Heisenberg group

2024/07/10 by I. A. Galyaev, Galyaev, I. A., Yu. L. Sachkov +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Optimization and Control (math.OC) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.07379

openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Three left-invariant Lorentzian problems on the Heisenberg group are considered. The Pontryagin maximum principle was applied to both problems and a parameterization of abnormal and normal extremal trajectories was obtained. Reachability sets and the existence of optimal trajectories are investigated.

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