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Program Systems: Theory and Applications, 2015, Volume 6, Issue 2, Pages 45–61 (Mi ps168)  

This article is cited in 2 scientific papers (total in 2 papers)

Optimization Methods and Control Theory

On the free Carnot (2,3,5,8) group

J.-P. Gauthiera, Yu. L. Sachkovb

a Laboratoire des Sciences de l’Information et des Systèmes, UMR, CNRS, France
b Ailamazyan Program System Institute of RAS

Abstract: We consider the free nilpotent Lie algebra $L$ with 2 generators, of step 4, and the corresponding connected simply connected Lie group $G$, with the aim to study the left-invariant sub-Riemannian structure on $G$ defined by the generators of $L$ as an orthonormal frame.
We compute two vector field models of $L$ by polynomial vector fields in $\mathbb{R}^8$, and find an infinitesimal symmetry of the sub-Riemannian structure. Further, we compute explicitly the product rule in $G$ and the right-invariant frame on $G$.

Key words and phrases: sub-Riemannian geometry, Carnot group.

Full text: PDF file (1365 kB)
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Document Type: Article
UDC: 517.977
MSC: 53C17
Received: 26.04.2015
Accepted: 20.05.2015
Language: English

Citation: J.-P. Gauthier, Yu. L. Sachkov, “On the free Carnot (2,3,5,8) group”, Program Systems: Theory and Applications, 6:2 (2015), 45–61

Citation in format AMSBIB
\Bibitem{GauSac15}
\by J.-P.~Gauthier, Yu.~L.~Sachkov
\paper On the free Carnot (2,3,5,8) group
\jour Program Systems: Theory and Applications
\yr 2015
\vol 6
\issue 2
\pages 45--61
\mathnet{http://mi.mathnet.ru/ps168}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. I. Pirshtuk, “O kharakteristicheskikh raspredeleniyakh levoinvariantnykh zadach optimalnogo upravleniya”, Tr. In-ta matem., 25:2 (2017), 70–81  mathnet
    2. L. V. Lokutsievskiy, Yu. L. Sachkov, “Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater”, Sb. Math., 209:5 (2018), 672–713  mathnet  crossref  crossref  adsnasa  isi  elib
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