Geodesics in the Engel Group with a Sub-Lorentzian Metric — the Space-Like Case

Qihui Cai

doi:10.1007/s11401-019-0191-z

Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (1) : 147 -162. DOI: 10.1007/s11401-019-0191-z

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Geodesics in the Engel Group with a Sub-Lorentzian Metric — the Space-Like Case

Qihui Cai ¹^,^a

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Abstract

Let E be the Engel group and D be a bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, the author constructs a parametrization of a quasi-pendulum equation by Jacobi functions, and then gets the space-like Hamiltonian geodesics in the Engel group with a sub-Lorentzian metric.

Keywords

Sub-Lorentzian metric / Engel Group / Geodesics

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Qihui Cai. Geodesics in the Engel Group with a Sub-Lorentzian Metric — the Space-Like Case. Chinese Annals of Mathematics, Series B, 2020, 41(1): 147-162 DOI:10.1007/s11401-019-0191-z