Characterizations of Hamiltonian geodesics in sub-Riemannian geometry

DOI10.1007/BF02463257zbMath0941.53023WikidataQ115392144 ScholiaQ115392144MaRDI QIDQ1972747

M. Alcheikh, Fernand Pelletier, Patrice Orro

Publication date: 13 April 2000

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

zbMATH Keywords

Lie grouptotally geodesic submanifoldsub-Riemannian manifoldabnormal geodesicsHamiltonian geodesic

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Foliations (differential geometric aspects) (53C12) Differential geometry of symmetric spaces (53C35) Sub-Riemannian geometry (53C17)

Related Items (6)

On sub-Riemannian and Riemannian structures on the Heisenberg groups ⋮ A contact covariant approach to optimal control with applications to sub-Riemannian geometry ⋮ Why are normal sub-Riemannian extremals locally minimizing? ⋮ Generic singularities of distributions of codimension 2 and bi-Hamiltonian structures ⋮ Localization of abnormal curves and pairs of Poisson tensors in low dimension ⋮ Optimal curves for an affine distribution

Cites Work

• The imbedding problem for Riemannian manifolds
• Large deviations and the Malliavin calculus
• Sub-Riemannian geometry
• Some regularity theorems for Carnot-Caratheodory metrics
• Singular extremals on Lie groups
• A note on Carnot geodesics in nilpotent Lie groups
• Abnormal Minimizers
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