Metric Lines in the Space of Curves
Differential Geometry
2025-11-27 v1
Abstract
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 geodesics, in the -jet space of plane curves. This result provides an initial contribution toward the broader classification of metric lines in jet spaces. Additionally, we present precise criteria, which characterize when a sub-Riemannian geodesic in the -jet space of plane curves can be identified as a metric line.
Keywords
Cite
@article{arxiv.2511.21065,
title = {Metric Lines in the Space of Curves},
author = {Daniella Catalá and Miriam Vollmayr-Lee and Alejandro Bravo-Doddoli},
journal= {arXiv preprint arXiv:2511.21065},
year = {2025}
}