TY - JOUR

T1 - Discretization of the sub-Riemannian Heisenberg Group

AU - Malkovich, Evgeny G.

N1 - The research was carried out within the framework of a state assignment of the Ministry of Education and Science of the Russian Federation for the Sobolev Institute of Mathematics of the SBRAS (project no. FWNF-2022-0006).

PY - 2025

Y1 - 2025

N2 - In this article, we present a discrete model of the sub-Riemannian Heisenberg group ℋ, which serves as an analog of a triangulation of a two-dimensional surface embedded in ℝ3. The constructed discrete model is represented by a spatial graph Γr with weighted edges. The shortest paths within Γr approximate geodesics in ℋ.

AB - In this article, we present a discrete model of the sub-Riemannian Heisenberg group ℋ, which serves as an analog of a triangulation of a two-dimensional surface embedded in ℝ3. The constructed discrete model is represented by a spatial graph Γr with weighted edges. The shortest paths within Γr approximate geodesics in ℋ.

KW - Heisenberg group

KW - Nonholonomic distribution

KW - computational geometry

KW - discrete geometry

KW - geodesics

KW - shortest paths in a graph

KW - sub-Riemannian spheres

KW - tortuosity

UR - https://www.scopus.com/pages/publications/105046213212

UR - https://www.mendeley.com/catalogue/8c355471-2999-33e7-9ac1-3334c1047522/

U2 - 10.56994/ARMJ.011.003.001

DO - 10.56994/ARMJ.011.003.001

M3 - Article

VL - 11

SP - 1

EP - 16

JO - Arnold Mathematical Journal

JF - Arnold Mathematical Journal

SN - 2199-6806

IS - 3

M1 - 1

ER -