The step-2 nilpotent \((n,n(n+1)/2)\) sub-Riemannian geometry

DOI10.1007/s10450-006-0380-4zbMath1111.49019OpenAlexW2022969651WikidataQ115384734 ScholiaQ115384734MaRDI QIDQ867454

A. Anzaldo-Meneses, Felipe Monroy-Pérez

Publication date: 15 February 2007

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

Full work available at URL: https://doi.org/10.1007/s10450-006-0380-4

zbMATH Keywords

geodesicsexponential mappingnilpotent Lie algebrasextremal curvessub-Riemannian

Mathematics Subject Classification ID

Related Items (6)

Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions ⋮ On the cut locus of free, step two Carnot groups ⋮ Free nilpotent Lie algebras admitting ad-invariant metrics ⋮ Maxwell strata in sub-Riemannian problem on the group of motions of a plane ⋮ On the subRiemannian cut locus in a model of free two-step Carnot group ⋮ Control theory on Lie groups

Cites Work

• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems
• Local invariants of smooth control systems
• Nilpotent \((3, 6)\) sub-Riemannian problem
• Optimal control on the Heisenberg group
• Controllability Along a Trajectory: A Variational Approach
• Nilpotent Approximations of Control Systems and Distributions
• Geometry of 2-Step Nilpotent Groups with a Left Invariant Metric. II
• Abnormal Minimizers
• Geometry of $2$-step nilpotent groups with a left invariant metric
• Shortest paths for sub-Riemannian metrics on rank-two distributions
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