A note on Carnot geodesics in nilpotent Lie groups

DOI10.1007/BF02255895zbMath0941.53029arXivmath/9505217OpenAlexW2077772528WikidataQ115392649 ScholiaQ115392649MaRDI QIDQ1972703

Ron Karidi, Christophe Golé

Publication date: 13 April 2000

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

Full work available at URL: https://arxiv.org/abs/math/9505217

zbMATH Keywords

nilpotent Lie groupsabnormal geodesicsCarnot geodesics

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Nilpotent and solvable Lie groups (22E25) Differential geometry of symmetric spaces (53C35)

Related Items (19)

Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups ⋮ Sard property for the endpoint map on some Carnot groups ⋮ Extremal curves in nilpotent Lie groups ⋮ Pliability, or the Whitney extension theorem for curves in Carnot groups ⋮ A dynamical approach to the Sard problem in Carnot groups ⋮ Extremals in some classes of Carnot groups ⋮ Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups ⋮ Some properties of abnormal extremals on Lie groups ⋮ Characterizations of Hamiltonian geodesics in sub-Riemannian geometry ⋮ MASS TRANSPORTATION IN GROUPS OF TYPE H ⋮ ODE trajectories as abnormal curves in Carnot groups ⋮ Geometric analysis on quaternion anisotropic Carnot groups ⋮ Sub-Riemannian geodesics on the three-dimensional solvable non-nilpotent Lie group \(\mathrm{SOLV}^-\) ⋮ Counter example to the Besicovitch covering property for some Carnot groups equipped with their Carnot-Carathéodory metric ⋮ Left-Invariant Sub-Riemannian Engel Structures: Abnormal Geodesics and Integrability ⋮ Non-minimality of corners in subriemannian geometry ⋮ Homogeneous spaces with inner metric and with integrable invariant distributions ⋮ Homogeneous spaces with inner metric and with integrable invariant distributions ⋮ Sub-Riemannian geometry on infinite-dimensional manifolds

Cites Work

• Unnamed Item
• On Carnot-Caratheodory metrics
• Sub-Riemannian geometry
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Some regularity theorems for Carnot-Caratheodory metrics
• Rigidity of integral curves of rank 2 distributions
• Geometry of balls in nilpotent Lie groups
• Singular extremals on Lie groups
• Abnormal Minimizers

This page was built for publication: A note on Carnot geodesics in nilpotent Lie groups