Geodesics in the Engel Group with a Sub-Lorentzian Metric |
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| Authors: | Qihui Cai Tiren Huang Yu L Sachkov Xiaoping Yang |
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| Affiliation: | 1.Department of Applied Mathematics,Nanjing University of Science and Technology,Nanjing,China;2.Department of Mathematics,Zhejiang Sci-Tech University,Hangzhou,China;3.Program Systems Institute,Yaroslav,Russia |
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| Abstract: | Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first study some properties of horizontal curves on E. Second, we prove that time-like normal geodesics are locally maximizers in the Engel group and calculate the explicit expression of non-space-like geodesics. |
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