Geodesics in the Heisenberg group \(H ^{n }\) with a Lorentzian metric
type: Item
instance of: scholarly article
title: Geodesics in the Heisenberg group \(H ^{n }\) with a Lorentzian metric
zbMATH Open document ID: 1261.58009
author: Ti-Ren Huang
author: Xiao-Ping Yang
published in: Journal of Dynamical and Control Systems
publication date: 2013-01-04T00:00:00Z
review text: 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.
reviewed by: Vladimir Balan
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 6122050
zbMATH Keywords: geodesics
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Lorentz metric
zbMATH Keywords: conjugate locus
zbMATH Keywords: sub-Lorentzian structure
zbMATH Keywords: reachable sets
MaRDI profile type: Publication
full work available at URL: s10883-012-9156-1
OpenAlex ID: W2067992245
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DOI: 10.1007/S10883-012-9156-1
description: scientific article; zbMATH DE number 6122050