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## Reachable sets for a class of contact sub-lorentzian metrics on $\mathbb{R}^{3}$, and null non-smooth geodesics

### Volume 82 / 2008

Banach Center Publications 82 (2008), 101-110 MSC: 53C50. DOI: 10.4064/bc82-0-7

#### Abstract

We compute future timelike and nonspacelike reachable sets from the origin for a class of contact sub-Lorentzian metrics on $\mathbb{R}% ^{3}$. 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.

#### Authors

• Marek GrochowskiFaculty of Mathematics and Natural Sciences
Cardinal Stefan Wyszyński University
Dewajtis 5
01-815 Warszawa, Poland
e-mail

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