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Geodesics in the Engel Group with a Sub-Lorentzian Metric——the Space-Like Case 被引量:1

Geodesics in the Engel Group with a Sub-Lorentzian Metric——the Space-Like Case
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摘要 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. 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.
作者 Qihui CAI
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2020年第1期147-162,共16页 数学年刊(B辑英文版)
基金 supported by the Science and Technology Development Fund of Nanjing Medical University(No.2017NJMU005).
关键词 Sub-Lorentzian METRIC Engel GROUP GEODESICS Sub-Lorentzian metric Engel Group Geodesics
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