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Discretization of the sub-Riemannian Heisenberg Group. / Malkovich, Evgeny G.

In: Arnold Mathematical Journal, Vol. 11, No. 3, 1, 2025, p. 1-16.

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

Harvard

Malkovich, EG 2025, 'Discretization of the sub-Riemannian Heisenberg Group', Arnold Mathematical Journal, vol. 11, no. 3, 1, pp. 1-16. https://doi.org/10.56994/ARMJ.011.003.001

APA

Malkovich, E. G. (2025). Discretization of the sub-Riemannian Heisenberg Group. Arnold Mathematical Journal, 11(3), 1-16. [1]. https://doi.org/10.56994/ARMJ.011.003.001

Vancouver

Malkovich EG. Discretization of the sub-Riemannian Heisenberg Group. Arnold Mathematical Journal. 2025;11(3):1-16. 1. doi: 10.56994/ARMJ.011.003.001

Author

Malkovich, Evgeny G. / Discretization of the sub-Riemannian Heisenberg Group. In: Arnold Mathematical Journal. 2025 ; Vol. 11, No. 3. pp. 1-16.

BibTeX

@article{ce2004404e6f4ff99f4cad4dc4f6c178,
title = "Discretization of the sub-Riemannian Heisenberg Group",
abstract = "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.",
keywords = "Heisenberg group, Nonholonomic distribution, computational geometry, discrete geometry, geodesics, shortest paths in a graph, sub-Riemannian spheres, tortuosity",
author = "Malkovich, {Evgeny G.}",
note = "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).",
year = "2025",
doi = "10.56994/ARMJ.011.003.001",
language = "English",
volume = "11",
pages = "1--16",
journal = "Arnold Mathematical Journal",
issn = "2199-6806",
number = "3",

}

RIS

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 -

ID: 81555340