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Geodesics in the Engel group with a sub-Lorentzian metric (1506.06127v1)
Published 18 Jun 2015 in math.OC
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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