34 citations · 50 across the 12 of their papers we have counts for
6 papers · 1 filter
Optimal Synthesis on the Special Linear Group
Marcus T. C. Lau, Alejandro Bravo-Doddoli
We study the exponential map on the group of real two-by-two matrices with determinant one, endowed with a left-invariant Riemannian metric. Using the Euler-Poincaré equation and i…
Metric Lines in the Space of Curves
Daniella Catalá, Miriam Vollmayr-Lee, Alejandro Bravo-Doddoli
This paper investigates sub-Riemannian geodesics in the jet space of curves. We establish the existence of two distinct families of metric lines, that is, globally minimizing geode…
Integrable sub-Riemannian geodesic flows on the special orthogonal group
Alejandro Bravo-Doddoli, Philip Arathoon, Anthony M. Bloch
We analyse the geometry of the rubber-rolling distribution on the special orthogonal group and show that almost all the normal geodesics of any right-invariant sub-Riemannian metri…
Metric Lines in the Special Euclidean group on the plane
Y. Wang, S. Ku, A. Bravo-Doddoli
The Special Euclidean group on the plane has the left-invariant sub-Riemannian structure. Every sub-Riemannian manifold possesses a Hamiltonian function governing the sub-R…
Metric Lines in Engel-type Groups
Alejandro Bravo-Doddoli
In the framework of sub-Riemannian manifolds, a natural question is: What are the ''metric lines'' (i.e., isometric embeddings of the real line)? This article presents a conjecture…
Sympletic reduction of the sub-Riemannian geodesic flow for metabelian nilpotent groups
Alejandro Bravo-Doddoli, Enrico Le Donne, Nicola Paddeu
We consider nilpotent Lie groups for which the derived subgroup is abelian. We equip them with subRiemannian metrics and we study the normal Hamiltonian flow on the cotangent bundl…