differential geometry

The Lorentzian Problem on the Group

arXiv:2607.11592

summary

The paper studies a left‑invariant Lorentzian metric on the Lie group SU(2), investigating controllability, existence of length‑maximizing curves, extremal trajectories, and curvature properties.

Abstract

We consider a left-invariant Lorentzian problem on SU(2). The following questions are addressed: complete controllability, existence of length maximizers, extremals, curvature.

Topics & keywords

#lorentzian geometry#lie groups#su(2)#geometric control#geodesics#curvatureleft-invariant Lorentzian metriccontrollabilitylength maximizersextremalscurvature
The Lorentzian Problem on the Group $SU(2)$ · wovepaper