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Geodesics in the Heisenberg group H n with a Lorentzian metric

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Abstract

Let \( {\mathbb{H}^n} \) be the Heisenberg group in \( {\mathbb{R}^{2n + 1 }} \) and D be a bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first study the reachable sets by the time-like future directed curves. Second, we give a complete description of the Hamiltonian geodesics. Third, we compute the time-like conjugate locus of the origin.

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Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing University of Science & Technology, Nanjing, 210094, P.R. China

    Tiren Huang & Xiaoping Yang

  2. School of Mathematical Sciences, USTC, Nanjing, P.R. China

    Tiren Huang

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  1. Tiren Huang
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  2. Xiaoping Yang
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Correspondence to Tiren Huang.

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Huang, T., Yang, X. Geodesics in the Heisenberg group H n with a Lorentzian metric. J Dyn Control Syst 18, 479–498 (2012). https://doi.org/10.1007/s10883-012-9156-1

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  • DOI: https://doi.org/10.1007/s10883-012-9156-1

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