SUB-LORETZIAN EXTREMALS DEFINED BY AN ANTINORM

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Abstract

We consider a left-invariant sub-Lorentzian structure on a Lie group. We assume that this structure is 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 that normal extremal trajectories keep their causal type. Tangent vectors of abnormal extremal trajectories are either light-like or tangent vectors of sub-Riemannian extremal trajectories for the sub-Riemannian distribution spanned by the cone.

About the authors

A. V Podobryaev

A.K. Ailamazyan Program Systems Institute of RAS

Email: alex@alex.botik.ru
Pereslavl-Zalesskiy, Russia

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