Published Paper

Inserted: 28 sep 2020
Last Updated: 16 feb 2024

Journal: ESAIM: Control, Optimisation and Calculus of Variations
Volume: 28
Number: 9
Pages: 24
Year: 2022

Abstract:

Given a surface $S$ in a 3D contact sub-Riemannian manifold $M$, we investigate the metric structure induced on $S$ by $M$, in the sense of length spaces. First, we define a coefficient $\widehat K$ at characteristic points that determines locally the characteristic foliation of $S$. Next, we identify some global conditions for the induced distance to be finite. In particular, we prove that the induced distance is finite for surfaces with the topology of a sphere embedded in a tight coorientable distribution, with isolated characteristic points.