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| Geodesics in the Engel Group with a Sub-Lorentzian Metric—— the Space-Like Case |
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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 |
| Page view： 699
Net amount： 787 |
Authors： |
Qihui CAI; |
Foundation： |
This work was supported by the Science and Technology
Development Fund of Nanjing Medical University (No.2017NJMU005). |
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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 |
Classification： |
58E10, 53C50 |
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