Article Dans Une Revue Journal of Dynamical and Control Systems Année : 2020

A metric interpretation of the geodesic curvature in the Heisenberg group

Résumé

In this paper we study the notion of geodesic curvature of smooth horizontal curves parametrized by arc lenght in the Heisenberg group, that is the simplest sub-Riemannian structure. Our goal is to give a metric interpretation of this notion of geodesic curvature as the first corrective term in the Taylor expansion of the distance between two close points of the curve.

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Dates et versions

hal-01916425 , version 1 (08-11-2018)
hal-01916425 , version 2 (12-11-2018)
hal-01916425 , version 3 (27-02-2019)

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Mathieu Kohli. A metric interpretation of the geodesic curvature in the Heisenberg group. Journal of Dynamical and Control Systems, 2020, 26 (1), pp.159-174. ⟨10.1007/s10883-019-09444-7⟩. ⟨hal-01916425v3⟩
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