Geodesics in the Heisenberg group \(H ^{n }\) with a Lorentzian metric
The sub-Lorentzian structure (\(M\), \(D\), \(g\)) is considered, where \(M=\mathbb{H}^n\) is the Heisenberg group in \(\mathbb{R}^{2n+1}\), \(D\) is a bracket generating a left-invariant distribution on \(M\), and \(g\) is a Lorentzian metric of index 1 on \(D\). In this framework, the three-fold goal of the paper is to study the reachable sets by the time-like future-directed curves, to completely describe the Hamiltonian geodesics, and to compute the time-like conjugate locus of the origin.
scientific article; zbMATH DE number 6122050
scientific article