Horizontal Joinability in Canonical 3-Step Carnot Groups with Corank 2 Horizontal Distributions

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Horizontal Joinability in Canonical 3-Step Carnot Groups with Corank 2 Horizontal Distributions. / Greshnov, A. V.; Zhukov, R. I.

In: Siberian Mathematical Journal, Vol. 62, No. 4, 07.2021, p. 598-606.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{d5db692eb8ea466eb740b164b94dc8b0,

title = "Horizontal Joinability in Canonical 3-Step Carnot Groups with Corank 2 Horizontal Distributions",

abstract = "We prove that on each 2-step Carnot group with a corank 1 horizontal distributiontwo arbitrary points can be joined with a horizontal broken line consisting of at most 3 segments,while on every canonical 3-step Carnot group G with a corank 2 horizontal distribution two arbitrary pointscan be joined with a horizontal broken line consisting of at most 7 segments.We show thattwo arbitrary points in the center of G are joined by infinitely many horizontal broken lines with 4 segments.Here by a segment of a horizontal broken linewe mean a segment of an integral lineof some left-invariant horizontal vector fieldthat is a linear combination of left-invariant horizontal basis vector fields of the Carnot group.",

keywords = "517, Carnot group, horizontal broken line, left-invariant basis vector fields, Rashevskii–Chow theorem",

author = "Greshnov, {A. V.} and Zhukov, {R. I.}",

note = "Funding Information: The authors were supported by the Mathematical Center in Akademgorodok under Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = jul,

doi = "10.1134/S0037446621040030",

language = "English",

volume = "62",

pages = "598--606",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "4",

}

RIS

TY - JOUR

T1 - Horizontal Joinability in Canonical 3-Step Carnot Groups with Corank 2 Horizontal Distributions

AU - Greshnov, A. V.

AU - Zhukov, R. I.

N1 - Funding Information: The authors were supported by the Mathematical Center in Akademgorodok under Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/7

Y1 - 2021/7

N2 - We prove that on each 2-step Carnot group with a corank 1 horizontal distributiontwo arbitrary points can be joined with a horizontal broken line consisting of at most 3 segments,while on every canonical 3-step Carnot group G with a corank 2 horizontal distribution two arbitrary pointscan be joined with a horizontal broken line consisting of at most 7 segments.We show thattwo arbitrary points in the center of G are joined by infinitely many horizontal broken lines with 4 segments.Here by a segment of a horizontal broken linewe mean a segment of an integral lineof some left-invariant horizontal vector fieldthat is a linear combination of left-invariant horizontal basis vector fields of the Carnot group.

AB - We prove that on each 2-step Carnot group with a corank 1 horizontal distributiontwo arbitrary points can be joined with a horizontal broken line consisting of at most 3 segments,while on every canonical 3-step Carnot group G with a corank 2 horizontal distribution two arbitrary pointscan be joined with a horizontal broken line consisting of at most 7 segments.We show thattwo arbitrary points in the center of G are joined by infinitely many horizontal broken lines with 4 segments.Here by a segment of a horizontal broken linewe mean a segment of an integral lineof some left-invariant horizontal vector fieldthat is a linear combination of left-invariant horizontal basis vector fields of the Carnot group.

KW - 517

KW - Carnot group

KW - horizontal broken line

KW - left-invariant basis vector fields

KW - Rashevskii–Chow theorem

UR - http://www.scopus.com/inward/record.url?scp=85112638863&partnerID=8YFLogxK

U2 - 10.1134/S0037446621040030

DO - 10.1134/S0037446621040030

M3 - Article

AN - SCOPUS:85112638863

VL - 62

SP - 598

EP - 606

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -

ID: 33990520