Normal forms and reachable sets for analytic Martinet sub-Lorentzian structures of Hamiltonian type

DOI10.1007/s10883-011-9110-7zbMath1209.53018OpenAlexW2057994538WikidataQ125121307 ScholiaQ125121307MaRDI QIDQ628725

Juan-Miguel Gracia

Publication date: 14 March 2011

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10883-011-9110-7

zbMATH Keywords

reachable setscut locifuture null conjugatetime-like Hamiltonian geodesics

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (16)

Graph surfaces on five-dimensional sub-Lorentzian structures ⋮ The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure ⋮ Remarks on global sub-Lorentzian geometry ⋮ Sub-semi-Riemannian geometry of general \(H\)-type groups ⋮ Sub-Lorentzian coarea formula for mappings of Carnot groups ⋮ The area of graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ Two-step sub-Lorentzian structures and graph surfaces ⋮ Classes of maximal surfaces on Carnot groups ⋮ The area of graphs on arbitrary Carnot groups with sub-Lorentzian structure ⋮ Normal forms for sub-Lorentzian metrics supported on Engel type distributions ⋮ The structure of reachable sets and geometric optimality of singular trajectories for certain affine control systems in \(\mathbb R^{3}\). The sub-Lorentzian approach ⋮ Causality and topology in sub-Lorentzian geometry ⋮ Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ The area formula for graphs on 4-dimensional 2-step sub-Lorentzian structures ⋮ Geodesics in the Engel group with a sub-Lorentzian metric -- the space-like case ⋮ Unnamed Item

Cites Work

• Reachable sets for the Heisenberg sub-Lorentzian structure on \(\mathbb R^3\). An estimate for the distance function
• Properties of reachable sets in the sub-Lorentzian geometry
• Normal forms of germs of contact sub-Lorentzian structures on \(\mathbb R^3\). Differentiability of the sub-Lorentzian distance function
• Control theory from the geometric viewpoint.
• Sub-Riemannian sphere in Martinet flat case
• Unnamed Item
• Unnamed Item

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