Geodesics in the Engel group with a sub-Lorentzian metric

2015/06/18 by Cai, Qihui, Huang, Tiren, Sachkov, Yuri L. +1 · 1 citation
#53C50 #58E10 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1506.06127

Abstract

Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first study some properties of horizontal curves on E. Second, we prove that time-like normal geodesics are locally maximizers in the Engel group, and calculate the explicit expression of non-space-like geodesics.

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• Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group

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