English

Computational geometry in Heisenberg group Heis^3

Differential Geometry 2025-10-20 v1 Numerical Analysis Metric Geometry Numerical Analysis

Abstract

Among eight possible geometric structures on three-dimensional manifolds less studied from the differential geometric point of view are those modelled on the Heisenberg group Heis3Heis^3. We consider the Heisenberg left-invariant metric and use some results on Levi-Civita connection and curvature tensor to present solutions of equations for geodesic lines in the Heisenberg group. Using "Mathematica" software package we also present drawings of geodesic lines and metric balls in the Heisenberg group.

Keywords

Cite

@article{arxiv.math/0204105,
  title  = {Computational geometry in Heisenberg group Heis^3},
  author = {Andrey Marenich},
  journal= {arXiv preprint arXiv:math/0204105},
  year   = {2025}
}

Comments

4 pages, 5 figures

R2 v1 2026-07-22T16:44:26.759Z