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.
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This work was supported by the Science and Technology Development Fund of Nanjing Medical University (No. 2017NJMU005).
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Cai, Q. Geodesics in the Engel Group with a Sub-Lorentzian Metric — the Space-Like Case. Chin. Ann. Math. Ser. B 41, 147–162 (2020). https://doi.org/10.1007/s11401-019-0191-z
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DOI: https://doi.org/10.1007/s11401-019-0191-z