Title: Extremals in the Engel group with a sub-Lorentzian metric
Authors: A. A. Ardentov, Tiren Huang, Yu. L. Sachkov, Xiaoping Yang
Let E be the Engel group and D be a 2-dimensional bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1.
In this paper, we first prove that timelike normal extremals are locally maxiziming. Second, we get a description of abnormal extremal and obtain the parametrization of timelike, spacelike, lightlike normal extremal trajectories by Jacobi functions. Third, the discrete symmetry groups and its fixed points which are Maxwell points of of timelike and spacelike normal extremals, are described.
ArXiv ID (ENG): 1507.07326