3 papers
math.DG2025
Metric Lines in the Space of Curves
Daniella Catalá, Miriam Vollmayr-Lee, Alejandro Bravo-Doddoli
This paper investigates sub-Riemannian geodesics within the jet space of curves. We establish the existence of two distinct families of metric lines, that is, globally minimizing g…
math.DG2024
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…
math.DS2022
No Periodic normal Geodesics in
Alejandro Bravo-Doddoli
The space of -jets of real function of one real variable admits the structure of a Carnot group, which then has an associated Hamiltonian geodesic flow. As in any Hamilt…