Journal of Dynamical and Control Systems· 2026Q2
Metric Lines in Engel-Type Groups
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- Q2SCImago
- 2026year
Short summary
A new conjecture classifies metric lines (isometric embeddings of the real line) in Carnot groups, with a focus on Engel-type groups using a novel 'sequence method'.
AI-generated from the title and abstract; the full text is not read.
Key points
- Proposes a conjecture for classifying metric lines in Carnot groups.
- Focuses on Engel-type groups with an (n+1)-rank distribution.
- Introduces and applies the 'sequence method' for analysis.
- Addresses the question of isometric embeddings of the real line in sub-Riemannian settings.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract In the framework of sub-Riemannian manifolds, a natural question is: What are the “metric lines” (i.e., isometric embeddings of the real line)? This article presents a conjecture classifying metric lines in Carnot groups and investigates the question for Carnot groups of arbitrary rank. It focuses on metric lines in Engel-type groups, whose sub-Riemannian structure is defined on a distribution of rank $$n+1$$ . The approach employs a novel technique, the sequence method, initially developed to study metric lines in jet space.
The authors' abstract, as published at the source. Journal of Dynamical and Control Systems, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics