On the Heisenberg sub-Lorentzian metric on ℝ³
Marek Grochowski (2004)
Banach Center Publications
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In this paper we study properties of the Heisenberg sub-Lorentzian metric on ℝ³. We compute the conjugate locus of the origin, and prove that the sub-Lorentzian distance in this case is differentiable on some open set. We also prove the existence of regular non-Hamiltonian geodesics, a phenomenon which does not occur in the sub-Riemannian case.