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

Citation:

Qihui CAI.Geodesics in the Engel Group with a Sub-Lorentzian Metric—— the Space-Like Case[J].Chinese Annals of Mathematics B,2020,41(1):147~162
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Authors:

Qihui CAI;

Foundation:

This work was supported by the Science and Technology Development Fund of Nanjing Medical University (No.2017NJMU005).
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

Classification:

58E10, 53C50
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