On extensions of sub-Riemannian structures on Lie groups

DOI10.1016/j.difgeo.2016.02.001zbMath1337.53042OpenAlexW2267217655WikidataQ115355744 ScholiaQ115355744MaRDI QIDQ268426

Rory Biggs, Péter T. Nagy

Publication date: 15 April 2016

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2016.02.001

zbMATH Keywords

Lie groupsgeodesicssub-Riemannian geometry

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Existence theories for optimal control problems involving ordinary differential equations (49J15) Geodesics in global differential geometry (53C22) Sub-Riemannian geometry (53C17)

Related Items

On sub-Riemannian and Riemannian structures on the Heisenberg groups, Control systems on nilpotent Lie groups of dimension \(\leq 4\): equivalence and classification

Cites Work

• Sub-Riemannian structures on 3D Lie groups
• Extremal trajectories and Maxwell strata in sub-Riemannian problem on group of motions of pseudo-Euclidean plane
• Isometry groups on homogeneous nilmanifolds
• Some regularity theorems for Carnot-Caratheodory metrics
• Control theory from the geometric viewpoint.
• Geodesics and isometries of Carnot groups
• Cost-extended control systems on Lie groups
• Some remarks on the oscillator group
• Conjugate points in nilpotent sub-Riemannian problem on the Engel group
• On sub-Riemannian geodesics on the Engel groups: Hamilton's equations
• Extremal trajectories in a nilpotent sub-Riemannian problem on the Engel group
• Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane
• Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
• Maxwell strata in sub-Riemannian problem on the group of motions of a plane
• Left invariant metrics and curvatures on simply connected three-dimensional Lie groups
• Shortest paths for sub-Riemannian metrics on rank-two distributions
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces
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