Sub-Lorentzian distance and spheres on the Heisenberg group

TL;DR

This paper studies the sub-Lorentzian geometry on the Heisenberg group, deriving the optimal control synthesis, and explicitly describing the sub-Lorentzian distance and spheres.

Contribution

It provides the first explicit description of sub-Lorentzian spheres and distances on the Heisenberg group, advancing understanding of Lorentzian sub-Riemannian geometries.

Findings

Explicit optimal synthesis constructed

Sub-Lorentzian distance characterized

Spheres explicitly described

Abstract

The left-invariant sub-Lorentzian problem on the Heisenberg group is considered. An optimal synthesis is constructed, the sub-Lorentzian distance and spheres are described.