TY - JOUR

T1 - The Shortest Polygonal Chains in the Heisenberg Group

AU - Basalaev, S. G.

N1 - The work was supported by the Mathematical Center in Akademgorodok, agreement with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2022-282. Basalaev, S. G. The Shortest Polygonal Chains in the Heisenberg Group / S. G. Basalaev // Russian Mathematics. – 2024. – Vol. 68, No. 11. – P. 71-76. – DOI 10.3103/S1066369X24700907.

PY - 2025/2/18

Y1 - 2025/2/18

N2 - Abstract: We describe the shortest polygonal chains that connect two points on the first Heisenberg group with the sub-Riemannian structure. The shortest polygonal chain connecting two points with a fixed number of links either is a straight line or consists of segments of the same length such that the projections of their endpoints are inscribed in a circle. The analytical description is obtained for the spheres of the quasimetric generated by the shortest polygonal chains with three links.

AB - Abstract: We describe the shortest polygonal chains that connect two points on the first Heisenberg group with the sub-Riemannian structure. The shortest polygonal chain connecting two points with a fixed number of links either is a straight line or consists of segments of the same length such that the projections of their endpoints are inscribed in a circle. The analytical description is obtained for the spheres of the quasimetric generated by the shortest polygonal chains with three links.

KW - Heisenberg group

KW - polygonal chain

KW - shortest path

UR - https://www.mendeley.com/catalogue/85e64e08-4842-3504-b0ea-9596263538bc/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85219665204&origin=inward&txGid=71b4abc54e9a6b60d2bf4290c4703aa1

UR - https://elibrary.ru/item.asp?id=80348745

U2 - 10.3103/S1066369X24700907

DO - 10.3103/S1066369X24700907

M3 - Article

VL - 68

SP - 71

EP - 76

JO - Russian Mathematics

JF - Russian Mathematics

SN - 1066-369X

IS - 11

ER -