We compute future timelike and nonspacelike reachable sets from the origin for a class of contact sub-Lorentzian metrics on ℝ³. Then we construct non-smooth (and therefore non-Hamiltonian) null geodesics for these metrics. As a consequence we deduce that the sub-Lorentzian distance from the origin is continuous at points belonging to the boundary of the reachable set.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-7,
author = {Marek Grochowski},
title = {Reachable sets for a class of contact sub-lorentzian metrics on $\mathbb{R}$$^3$, and null non-smooth geodesics},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {101-110},
zbl = {1155.53035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-7}
}
Marek Grochowski. Reachable sets for a class of contact sub-lorentzian metrics on ℝ³, and null non-smooth geodesics. Banach Center Publications, Tome 83 (2008) pp. 101-110. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-7/