Horizontal Joinability on 5-Dimensional 2-Step Carnot Groups with a Codimension 2 Horizontal Distribution

Horizontal Joinability on 5-Dimensional 2-Step Carnot Groups with a Codimension 2 Horizontal Distribution

For a 5-dimensional 2-step Carnot group G 3,2 with a codimension 2 horizontal distribution, we prove that any two points u , v ∈ G 3,2 can be joined on it by a horizontal broken line consisting of at most three segments. A multi-dimensional generalization of this result is given.

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Veröffentlicht in:Algebra and logic 2023-05, Vol.62 (2), p.137-147
Hauptverfasser: Zhukov, R. I., Greshnov, A. V.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Group theory
Horizontal distribution
Lie algebras
Lie groups
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
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Zusammenfassung:For a 5-dimensional 2-step Carnot group G 3,2 with a codimension 2 horizontal distribution, we prove that any two points u , v ∈ G 3,2 can be joined on it by a horizontal broken line consisting of at most three segments. A multi-dimensional generalization of this result is given.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-024-09732-7