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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-4,
author = {Marek Grochowski},
title = {On the Heisenberg sub-Lorentzian metric on $\mathbb{R}$$^3$},
journal = {Banach Center Publications},
volume = {65},
year = {2004},
pages = {57-65},
zbl = {1065.53055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-4}
}
Marek Grochowski. On the Heisenberg sub-Lorentzian metric on ℝ³. Banach Center Publications, Tome 65 (2004) pp. 57-65. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-4/