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

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

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2021, Volume: 62, Number: 4, Pages: 598-606 Pages count : 9 DOI: 10.1134/S0037446621040030

Tags

517; Carnot group; horizontal broken line; left-invariant basis vector fields; Rashevskii–Chow theorem

Authors

Greshnov A.V. ¹ , Zhukov R.I. ²

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
2	Novosibirsk State University, Novosibirsk, Russian Federation

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. © 2021, Pleiades Publishing, Ltd.

Greshnov A.V. , Zhukov R.I.
Horizontal Joinability in Canonical 3-Step Carnot Groups with Corank 2 Horizontal Distributions
Siberian Mathematical Journal. 2021. V.62. N4. P.598-606. DOI: 10.1134/S0037446621040030 WOS Scopus OpenAlex

Greshnov A.V. , Zhukov R.I.
Горизонтальная соединимость на канонической 3-ступенчатой группе Карно с горизонтальным распределением коранга 2
Сибирский математический журнал. 2021. Т.62. №4. С.736–746. DOI: 10.33048/smzh.2021.62.403 OpenAlex

Web of science:	WOS:000682525600003
Scopus:	2-s2.0-85112638863
OpenAlex:	W3197563134

DB	Citing
Scopus	5
OpenAlex	6
Web of science	5