1. Metric lines in the jet space
- Author
-
Bravo-Doddoli Alejandro
- Subjects
carnot group ,jet space ,global minimizing geodesic ,sub-riemannian geometry ,53c17 ,53c22 ,49k15 ,20f65 ,22e25 ,Analysis ,QA299.6-433 - Abstract
In the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}), admits the structure of a Carnot group. Every Carnot group is sub-Riemannian manifold, so is Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}). This study aims to present a partial result about the classification of the metric lines within Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}). The method is to use an intermediate three-dimensional sub-Riemannian space RF3{{\mathbb{R}}}_{F}^{3} lying between the group Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}) and the Euclidean space R2{{\mathbb{R}}}^{2}.
- Published
- 2024
- Full Text
- View/download PDF