Geodesics in the Engel Group with a Sub-Lorentzian Metric — the Space-Like Case
Qihui Cai
Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (1) : 147 -162.
Geodesics in the Engel Group with a Sub-Lorentzian Metric — the Space-Like Case
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
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