Abstract

In this paper, we construct normal forms for sub-Lorentzian structures (H, g), where H is an analytic Martinet-type distribution on ?3 and g is an analytic Lorentzian metric on H, under the assumption that abnormal curves foliating the Martinet surface for H are timelike Hamiltonian geodesics. As an application, we compute reachable sets from a point for such structures. It turns out that such sets are described by four analytic functions and, consequently, they are semi-analytic. We also compute future null conjugate and cut loci, and the image under the exponential mapping for above-mentioned structures.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call