Title: Sub-Lorentzian Extremals Defined by an Antinorm

Authors: A.V.Podobryaev

Journal title: Differential Equations

Year: 2024

Issue: 3

Volume: 60

Pages: 361–373

Citation:

A.V. Podobryaev. Sub-Lorentzian Extremals Defined by an Antinorm // Differential Equations. 60, 3, 361–373 (2024)

Abstract:

We consider a left-invariant sub-Lorentzian structure on a Lie group. This structure is assumed to be defined by a closed convex salient cone in the corresponding Lie algebra and a continuous antinorm associated with this cone. We derive the Hamiltonian system for sub-
Lorentzian extremals and give conditions under which normal extremal trajectories keep their causal type. Tangent vectors of abnormal extremal trajectories are either lightlike or are tangent vectors of sub-Riemannian abnormal extremal trajectories for the sub-Riemannian distribution spanned by the cone.