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

Autor:	Glutsyuk, A., Sachkov, Yu.
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Dynamical Systems Mathematics - Optimization and Control 53C17 37C10 49K15
Druh dokumentu:	Working Paper
Popis:	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 $M$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.16065 Zobrazit plný text záznamu View this record from Arxiv