2024/05/13 by Alejandro Bravo-Doddoli, Bravo-Doddoli, Alejandro
Engineering · Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Optimization and Control (math.OC) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2405.08186
openalex publication_date 2024/05/13 · openalex created_date 2024/05/16 · openalex updated_date 2026/07/28
In the framework of sub-Riemannian Manifolds, a relevant question is: what are the \enquotemetric lines (i.e., the isometric embedding of the real line)? This article presents a conjecture classifying the metric lines in Carnot groups and takes the first steps in answering this question for \enquotearbitrary rank Carnot groups. We classify the metric lines of the Engel-type groups \Eng(n) (Theorem 1.2), whose sub-Riemannian structure is defined on a non-integrable distribution of rank n+1. Our approach is a new method, called the sequence method, which we began to develop to study metric lines in the jet space.