arXiv:2102.12741 Abstract | arXiv Analytics

arXiv:2102.12741 [math.DG]Abstract References Reviews Resources

Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case

Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat

Published 2021-02-25Version 1

We consider a closed three-dimensional contact sub-Riemannian manifold. The objective of this note is to provide a precise description of the sub-Riemannian geodesics with large initial momenta: we prove that they "spiral around the Reeb orbits", not only in the phase space but also in the configuration space. Our analysis is based on a normal form along any Reeb orbit due to Melrose.

Categories: math.DG, math.MG, math.SG

Keywords: 3d contact case, sub-riemannian geodesics, reeb flow, closed three-dimensional contact sub-riemannian manifold, reeb orbit

Related articles: Most relevant | Search more

arXiv:2405.14997 [math.DG] (Published 2024-05-23)

Metabelian distributions and sub-Riemannian geodesics

Enrico Le Donne, Nicola Paddeu, Alessandro Socionovo

arXiv:2203.04956 [math.DG] (Published 2022-03-09)

Derivatives of Sub-Riemannian Geodesics are $L_p$-Hölder Continuous

Lev Lokutsievskiy, Mikhail Zelikin

arXiv:2212.07615 [math.DG] (Published 2022-12-15)

Legendre singularities of sub-Riemannian geodesics

Goo Ishikawa, Yumiko Kitagawa