Computational geometry in Heisenberg group Heis3
Andrey Marenich
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 Heis3. 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.
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