ОПТИМАЛЬНЫЕ ОЦЕНКИ КОЛИЧЕСТВА ЗВЕНЬЕВ БАЗИСНЫХ ГОРИЗОНТАЛЬНЫХ ЛОМАНЫХ ДЛЯ 2-СТУПЕНЧАТЫХ ГРУПП КАРНО С ГОРИЗОНТАЛЬНЫМ РАСПРЕДЕЛЕНИЕМ КОРАНГА

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ОПТИМАЛЬНЫЕ ОЦЕНКИ КОЛИЧЕСТВА ЗВЕНЬЕВ БАЗИСНЫХ ГОРИЗОНТАЛЬНЫХ ЛОМАНЫХ ДЛЯ 2-СТУПЕНЧАТЫХ ГРУПП КАРНО С ГОРИЗОНТАЛЬНЫМ РАСПРЕДЕЛЕНИЕМ КОРАНГА. / Greshnov, Alexandr V.; Zhukov, Roman I.

в: Vestnik Rossiyskikh Universitetov. Matematika, Том 29, № 147, 2024, стр. 244-254.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{93269d18c7034ffb8e7e041114b97e05,

title = "ОПТИМАЛЬНЫЕ ОЦЕНКИ КОЛИЧЕСТВА ЗВЕНЬЕВ БАЗИСНЫХ ГОРИЗОНТАЛЬНЫХ ЛОМАНЫХ ДЛЯ 2-СТУПЕНЧАТЫХ ГРУПП КАРНО С ГОРИЗОНТАЛЬНЫМ РАСПРЕДЕЛЕНИЕМ КОРАНГА",

abstract = "For a 2-step Carnot group Dn, dim Dn = n + 1, with horizontal distribution of corank 1, we proved that the minimal number NXDn such that any two points u, v ∈ Dn can be joined by some basis horizontal k -broken line (i.e. a broken line consisting of k links) LXkDn (u, v), k ≤ NXDn , does not exeed n + 2. The examples of Dn such that NXDn = n + i, i = 1, 2, were found. Here XDn = {X1, . . ., Xn} is the set of left invariant basis horizontal vector fields of the Lie algebra of the group Dn, and every link of LXkDn (u, v) has the form exp(asXi)(w), s ∈ [0, s0], a = const.",

keywords = "2 -step Carnot groups, Rashevskii–Chow theorem, basis vector fields, broken lines, horizontal curves",

author = "Greshnov, {Alexandr V.} and Zhukov, {Roman I.}",

note = "The research was supported by the Russian Science Foundation (project no. 24-21-00319).",

year = "2024",

doi = "10.20310/2686-9667-2024-29-147-244-254",

language = "русский",

volume = "29",

pages = "244--254",

journal = "Vestnik Rossiyskikh Universitetov. Matematika",

issn = "2782-3342",

number = "147",

}

RIS

TY - JOUR

T1 - ОПТИМАЛЬНЫЕ ОЦЕНКИ КОЛИЧЕСТВА ЗВЕНЬЕВ БАЗИСНЫХ ГОРИЗОНТАЛЬНЫХ ЛОМАНЫХ ДЛЯ 2-СТУПЕНЧАТЫХ ГРУПП КАРНО С ГОРИЗОНТАЛЬНЫМ РАСПРЕДЕЛЕНИЕМ КОРАНГА

AU - Greshnov, Alexandr V.

AU - Zhukov, Roman I.

N1 - The research was supported by the Russian Science Foundation (project no. 24-21-00319).

PY - 2024

Y1 - 2024

N2 - For a 2-step Carnot group Dn, dim Dn = n + 1, with horizontal distribution of corank 1, we proved that the minimal number NXDn such that any two points u, v ∈ Dn can be joined by some basis horizontal k -broken line (i.e. a broken line consisting of k links) LXkDn (u, v), k ≤ NXDn , does not exeed n + 2. The examples of Dn such that NXDn = n + i, i = 1, 2, were found. Here XDn = {X1, . . ., Xn} is the set of left invariant basis horizontal vector fields of the Lie algebra of the group Dn, and every link of LXkDn (u, v) has the form exp(asXi)(w), s ∈ [0, s0], a = const.

AB - For a 2-step Carnot group Dn, dim Dn = n + 1, with horizontal distribution of corank 1, we proved that the minimal number NXDn such that any two points u, v ∈ Dn can be joined by some basis horizontal k -broken line (i.e. a broken line consisting of k links) LXkDn (u, v), k ≤ NXDn , does not exeed n + 2. The examples of Dn such that NXDn = n + i, i = 1, 2, were found. Here XDn = {X1, . . ., Xn} is the set of left invariant basis horizontal vector fields of the Lie algebra of the group Dn, and every link of LXkDn (u, v) has the form exp(asXi)(w), s ∈ [0, s0], a = const.

KW - 2 -step Carnot groups

KW - Rashevskii–Chow theorem

KW - basis vector fields

KW - broken lines

KW - horizontal curves

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85209734522&origin=inward&txGid=3650cc71cc55ab9b6cfa094015e2098a

UR - https://www.mendeley.com/catalogue/e49930aa-924a-3756-b4c2-e62fc0e86693/

U2 - 10.20310/2686-9667-2024-29-147-244-254

DO - 10.20310/2686-9667-2024-29-147-244-254

M3 - статья

VL - 29

SP - 244

EP - 254

JO - Vestnik Rossiyskikh Universitetov. Matematika

JF - Vestnik Rossiyskikh Universitetov. Matematika

SN - 2782-3342

IS - 147

ER -

ID: 61301328