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arXiv · 2009.11748

On the induced geometry on surfaces in 3D contact sub-Riemannian manifolds

Davide Barilari·Ugo Boscain·Daniele Cannarsa
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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.

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Davide Barilari, Ugo Boscain, Daniele Cannarsa. 2020-09-24. On the induced geometry on surfaces in 3D contact sub-Riemannian manifolds. https://doi.org/10.1051/cocv%2F2021104

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