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arXiv · 2102.12741

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

Yves Colin de Verdière·Luc Hillairet·Emmanuel Trélat
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Abstract

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.

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Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat. 2021-02-25. Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case. https://arxiv.org/abs/2102.12741

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