Sub-Riemannian geodesics on the Heisenberg 3D nil-manifold

A. Glutsyuk; Yu. Sachkov

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arXiv · 2406.16065

Sub-Riemannian geodesics on the Heisenberg 3D nil-manifold

A. Glutsyuk·Yu. Sachkov

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Abstract

We study the projection of the left-invariant sub-Riemannian structure on the 3D Heisenberg group $G$ to the Heisenberg 3D nil-manifold $M$ -- the compact homogeneous space of $G$ by the discrete Heisenberg group. First we describe dynamical properties of the geodesic flow for $M$: periodic and dense orbits, and a dynamical characterization of the normal Hamiltonian flow of Pontryagin maximum principle. Then we obtain sharp twoside bounds of sub-Riemannian balls and distance in $G$, and on this basis we estimate the cut time for sub-Riemannian geodesics in $M$.

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BibTeX RIS

A. Glutsyuk, Yu. Sachkov. 2024-06-23. Sub-Riemannian geodesics on the Heisenberg 3D nil-manifold. https://arxiv.org/abs/2406.16065

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