Chinese Annals of Mathematics, Series B

, Volume 41, Issue 1, pp 147–162 | Cite as

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

  • Qihui CaiEmail author


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.


Sub-Lorentzian metric Engel Group Geodesics 

2000 MR Subject Classification

58E10 53C50 


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© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2020

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, School of Biomedical Engineering and InformaticsNanjing Medical UniversityNanjingChina

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