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arXiv · 2511.21065

Metric Lines in the Space of Curves

Daniella Catalá·Miriam Vollmayr-Lee·Alejandro Bravo-Doddoli
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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 $2$-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 $2$-jet space of plane curves can be identified as a metric line.

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Daniella Catalá, Miriam Vollmayr-Lee, Alejandro Bravo-Doddoli. 2025-11-26. Metric Lines in the Space of Curves. https://arxiv.org/abs/2511.21065

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